In which direction do compass needles always align? Why?

Size: px
Start display at page:

Download "In which direction do compass needles always align? Why?"

Transcription

1 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 1 Complt t p ll: Mnt or s typ o or n t s stronst t t o t mnt. Tr r two typs o mnt pol: n. Wrt wt woul ppn twn t pols n o t mnt ntrtons low: Drw t mnt l lns on t r mnt low. Rmmr lns lwys strt t t n pont towrs t. Expln ow plottn ompss oul us to nvstt t mnt l roun mnt. You r vn t ollown quton n your xm: or = mnt lux nsty urrnt lnt A wr wt urrnt o 4.0A s pl twn two r mnts ( s wt o 12mm) n stt o ttrton. T mnt lux nsty s 0.2T. Clult t or tn on t wr. In w rton o ompss nls lwys ln? Wy? Not: n otr lultons, you my rqur to rrrn t ormul. Lst our mnt mtrls: Dn t trm mnt l : Stt t tor tt ts t strnt o t mnt l: Dsr t rn twn prmnnt mnt n n nu mnt. W o ts mnts wll xrt stronr or on mnt mtrl? A. B. l Wn urrnt lows trou onutn wr, mnt l s prou roun t wr. Stt two tors t strnt o t mnt l pns on: Expln your nswr.

2 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 2 A lon, strt onutn wr s pl vrtlly so tt t psss trou orzontl p o or. Dsr ow you woul us t p o qupmnt prvously stt to nvstt t mnt l you v rwn. How n you n t nort pol o solno? Wt s t motor t? Iron lns r sprnl onto t or. Drw t pttrn ty woul orm: Stt tr wys you n nrs t or: Wt s solno? Lst our wys n w you n m t mnt l roun solno/ ltromnt stronr: 3. Stt t p o qupmnt you oul us to nvstt t mnt l you v rwn ov. Drw t mnt l pttrn roun solno low: 3. How n you rvrs t rton o t or? l Stt t mto tt norms you o t rton o t urrnt n strt wr. 4. A motor s mnt lux nsty o 5T n urrnt o 8A. m Wt o your tum n nrs rprsnt n ts mto? tum: nrs: Dsr wt ppns to t mnt l roun strt wr wn t urrnt s rvrs. T totl lnt o t wr s 500m. Clult t or on t wr usn t quton F = BIL. Wt s ts pttrn smlr to?

3 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 3 You r vn t ollown quton n your xm. or = mnt lux nsty urrnt lnt Complt t tl: How n t rton o motor rvrs? Dsr ow you woul us n ron nl, lnt o nsult wr n ll to m n ltromnt tt n us to p up som stl ppr lps. Symol Prt o t Equton Wt It Rprsnts Unts How n t sp o motor nrs? or B Wt rul n us to n t rton o t or? Wy wll motor not wor wtout ommuttor? Wt nl o your tum, rst n son nr A n to t? Wt os prt rprsnt? L tum: rst nr: Dsr smpl ltr motor. son nr: Wt s t ss o n ltr motor?

4 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr Answrs 1 Complt t p ll: Mnt or s typ o non-ontt or n t s stronst t t pols o t mnt. Tr r two typs o mnt pol: nort pol n sout pol. Wrt wt woul ppn twn t pols n o t mnt ntrtons low: Drw t mnt l lns on t r mnt low. Rmmr lns lwys strt t t nort pol n pont towrs t sout pol. Expln ow plottn ompss oul us to nvstt t mnt l roun mnt. Pl t mnt on ln p o ppr. Pl t plottn ompss t on n/ov t pol o t mnt. Mr on t ppr wr t pont o t nl ponts. Mov t ompss to t pl you v ust mr. Rpt untl you v mov to t otr pol o t mnt. Rpt on t otr lnt o t mnt (.. top n tn ottom). You r vn t ollown quton n your xm: or = mnt lux nsty urrnt lnt A wr wt urrnt o 4.0A s pl twn two r mnts ( s wt o 12mm) n stt o ttrton. T mnt lux nsty s 0.2T. Clult t or tn on t wr. rpulson ttrton Lst our mnt mtrls: ron stl In w rton o ompss nls lwys ln? Wy? Mnt nort, us t rt s mnt l. Ts s possly u to t ron ontnt n t or. Not: n otr lultons, you my rqur to rrrn t ormul. onvrt 12mm nto mtrs = 0.012m pl vlus nto quton: or = 0.2T 4.0A 0.012m or = N (nwtons) Dn t trm mnt l : T ron roun mnt wr or ts on notr mnt or on mnt mtrl. Stt t tor tt ts t strnt o t mnt l: rpulson T strnt o t mnt l pns on t stn rom t mnt. 3. nl 4. olt Dsr t rn twn prmnnt mnt n n nu mnt. Prmnnt mnts prou tr own mnt l. Inu mnts om mnt wn pl n mnt l. Howvr, wn rmov rom t mnt l, n nu mnt loss most/ll o ts mntsm quly. W o ts mnts wll xrt stronr or on mnt mtrl? B A. B. Expln your nswr. B s mor lns o mnt lux. Wn urrnt lows trou onutn wr, mnt l s prou roun t wr. Stt two tors t strnt o t mnt l pns on: sz o t urrnt stn rom t wr

5 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr Answrs 2 A lon, strt onutn wr s pl vrtlly so tt t psss trou orzontl p o or. Iron lns r sprnl onto t or. Drw t pttrn ty woul orm: Dsr ow you woul us t p o qupmnt prvously stt to nvstt t mnt l you v rwn. Pl mnt ompss t on pont lon t wr. Turn t powr supply on n o. Mov t mnt ompss urtr lon t wr. An, turn t powr supply on n o. Mov t ompss urtr wy rom t wr to s tt t mnt l s wr. How n you n t nort pol o solno? Usn t rt-n rp mto. Hol t solno wt your rt n n nrs pontn n t rton t urrnt s lown. Your tum soul pont to t nort pol. Wt s t motor t? I onutor rryn urrnt s pl n mnt l, t mnt proun t l n t onutor xrt or on otr. Stt tr wys you n nrs t or: Inrsn t sz o t urrnt. Inrsn t lnt o t onutor n t Stt t p o qupmnt you oul us to nvstt t mnt l you v rwn ov. plottn ompss Wt s solno? A solno s orm wn lon p o onutn (n nsult) wr s loop nto ol ylnr. Drw t mnt l pttrn roun solno low: Lst our wys n w you n m t mnt l roun solno/ ltromnt stronr: Us lrr urrnt. Us n ron or. 3. A mor turns to t wr. 4. Pl t turns o t wr losr totr. mnt l. 3. Inrsn t lux nsty. How n you rvrs t rton o t or? By rvrsn t rton o t urrnt or rvrsn t rton o t mnt l. l Stt t mto tt norms you o t rton o t urrnt n strt wr. Rt-n rp mto/rul. A motor s mnt lux nsty o 5T n urrnt o 8A. m Wt o your tum n nrs rprsnt n ts mto? tum: T rton o t urrnt. nrs: T rton t l lns soul rwn. Wt s ts pttrn smlr to? Dsr wt ppns to t mnt l roun strt wr wn t urrnt s rvrs. T mnt l s lso rvrs. T totl lnt o t wr s 500m. Clult t or on t wr usn t quton F = BIL. onvrt m nto mtrs = 5m pl vlus nto quton: or = 5T 8.0A 5m T mnt l roun r mnt. or = 60N (nwtons)

6 AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 3 You r vn t ollown quton n your xm. or = mnt lux nsty urrnt lnt Complt t tl: Symol Prt o t Equton Wt It Rprsnts Unts F or N How n t rton o motor rvrs? By rvrsn t rton o t urrnt or rvrsn t rton o t mnt l. How n t sp o motor nrs? By nrsn t sz o t urrnt or nrsn t mnt l/us lrr mnt. Dsr ow you woul us n ron nl, lnt o nsult wr n ll to m n ltromnt tt n us to p up som stl ppr lps. Wrp t wr roun t ron nl. Connt t wr to t powr supply (wt onntn ls n rool lps). Swt on t powr supply. Us -mnts ppr lps. Suspn t nl nr t pprlps n ror ow mny ollt. T mor pprlps suspn, t stronr t ltromnt s. Cn t numr o turns (on t ol). Cn t urrnt (trou t ol). B mnt lux nsty I urrnt A L Lnt o t wr wtn t l. Wt s t ss o n ltr motor? A ol o wr rryn urrnt n mnt l tns to rott. T m Wt rul n us to n t rton o t or? Flmn s lt-n rul Wt nl o your tum, rst n son nr n to t? 90 Wt os prt rprsnt? tum: movmnt rst nr: l son nr: urrnt Wy wll motor not wor wtout ommuttor? T ommuttor nsurs tt t urrnt stys n t sm rton. Also t ol woul not r to spn. Ts mns t ol woul rmn stll n not rott. Dsr smpl ltr motor. A ol o wr s x (on n xl). T ns o t wr r onnt v splt-rn ommuttor. To ttry/powr supply. T ron rus ontts t t ommuttor nsurs t urrnt rton n t ol s lwys t sm. T ol s pl twn two (lt) mnts. Wt oppost pols n otr. T ol rotts ontnuously n ts s t ss o n ltr motor.

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees /1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our

More information

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson

More information

Lecture 20: Minimum Spanning Trees (CLRS 23)

Lecture 20: Minimum Spanning Trees (CLRS 23) Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss

More information

The University of Sydney MATH 2009

The University of Sydney MATH 2009 T Unvrsty o Syny MATH 2009 APH THEOY Tutorl 7 Solutons 2004 1. Lt t sonnt plnr rp sown. Drw ts ul, n t ul o t ul ( ). Sow tt s sonnt plnr rp, tn s onnt. Du tt ( ) s not somorp to. ( ) A onnt rp s on n

More information

Weighted Graphs. Weighted graphs may be either directed or undirected.

Weighted Graphs. Weighted graphs may be either directed or undirected. 1 In mny ppltons, o rp s n ssot numrl vlu, ll wt. Usully, t wts r nonntv ntrs. Wt rps my tr rt or unrt. T wt o n s otn rrr to s t "ost" o t. In ppltons, t wt my msur o t lnt o rout, t pty o ln, t nry rqur

More information

d e c b a d c b a d e c b a a c a d c c e b

d e c b a d c b a d e c b a a c a d c c e b FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count

More information

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1 Spnnn Trs BFS, DFS spnnn tr Mnmum spnnn tr Mr 28, 2018 Cn Hrn / Gory Tn 1 Dpt-rst sr Vsts vrts lon snl pt s r s t n o, n tn ktrks to t rst junton n rsums own notr pt Mr 28, 2018 Cn Hrn / Gory Tn 2 Dpt-rst

More information

Platform Controls. 1-1 Joystick Controllers. Boom Up/Down Controller Adjustments

Platform Controls. 1-1 Joystick Controllers. Boom Up/Down Controller Adjustments Ston 7 - Rpr Prours Srv Mnul - Son Eton Pltorm Controls 1-1 Joystk Controllrs Mntnn oystk ontrollrs t t propr sttns s ssntl to s mn oprton. Evry oystk ontrollr soul oprt smootly n prov proportonl sp ontrol

More information

SAMPLE CSc 340 EXAM QUESTIONS WITH SOLUTIONS: part 2

SAMPLE CSc 340 EXAM QUESTIONS WITH SOLUTIONS: part 2 AMPLE C EXAM UETION WITH OLUTION: prt. It n sown tt l / wr.7888l. I Φ nots orul or pprotng t vlu o tn t n sown tt t trunton rror o ts pproton s o t or or so onstnts ; tt s Not tt / L Φ L.. Φ.. /. /.. Φ..787.

More information

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling.

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling. Cptr 4 4 Intrvl Suln Gry Alortms Sls y Kvn Wyn Copyrt 005 Prson-Ason Wsly All rts rsrv Intrvl Suln Intrvl Suln: Gry Alortms Intrvl suln! Jo strts t s n nss t! Two os omptl ty on't ovrlp! Gol: n mxmum sust

More information

Depth First Search. Yufei Tao. Department of Computer Science and Engineering Chinese University of Hong Kong

Depth First Search. Yufei Tao. Department of Computer Science and Engineering Chinese University of Hong Kong Dprtmnt o Computr Sn n Ennrn Cns Unvrsty o Hon Kon W v lry lrn rt rst sr (BFS). Toy, w wll suss ts sstr vrson : t pt rst sr (DFS) lortm. Our susson wll on n ous on rt rps, us t xtnson to unrt rps s strtorwr.

More information

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices. Cptr 11: Trs 11.1 - Introuton to Trs Dnton 1 (Tr). A tr s onnt unrt rp wt no sp ruts. Tor 1. An unrt rp s tr n ony tr s unqu sp pt twn ny two o ts vrts. Dnton 2. A root tr s tr n w on vrtx s n snt s t

More information

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e) POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly

More information

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths. How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0

More information

Having a glimpse of some of the possibilities for solutions of linear systems, we move to methods of finding these solutions. The basic idea we shall

Having a glimpse of some of the possibilities for solutions of linear systems, we move to methods of finding these solutions. The basic idea we shall Hvn lps o so o t posslts or solutons o lnr systs, w ov to tos o nn ts solutons. T s w sll us s to try to sply t syst y lntn so o t vrls n so ts qutons. Tus, w rr to t to s lnton. T prry oprton nvolv s

More information

(Minimum) Spanning Trees

(Minimum) Spanning Trees (Mnmum) Spnnn Trs Spnnn trs Kruskl's lortm Novmr 23, 2017 Cn Hrn / Gory Tn 1 Spnnn trs Gvn G = V, E, spnnn tr o G s onnt surp o G wt xtly V 1 s mnml sust o s tt onnts ll t vrts o G G = Spnnn trs Novmr

More information

CMSC 451: Lecture 4 Bridges and 2-Edge Connectivity Thursday, Sep 7, 2017

CMSC 451: Lecture 4 Bridges and 2-Edge Connectivity Thursday, Sep 7, 2017 Rn: Not ovr n or rns. CMSC 451: Ltr 4 Brs n 2-E Conntvty Trsy, Sp 7, 2017 Hr-Orr Grp Conntvty: (T ollown mtrl ppls only to nrt rps!) Lt G = (V, E) n onnt nrt rp. W otn ssm tt or rps r onnt, t somtms t

More information

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms

Exam 2 Solutions. Jonathan Turner 4/2/2012. CS 542 Advanced Data Structures and Algorithms CS 542 Avn Dt Stutu n Alotm Exm 2 Soluton Jontn Tun 4/2/202. (5 ont) Con n oton on t tton t tutu n w t n t 2 no. Wt t mllt num o no tt t tton t tutu oul ontn. Exln you nw. Sn n mut n you o u t n t, t n

More information

DOCUMENT STATUS: RELEASE

DOCUMENT STATUS: RELEASE RVSON STORY RV T SRPTON O Y 0-4-0 RLS OR PROUTON 5 MM -04-0 NS TRU PLOT PROUTON -- S O O OR TLS 30 MM 03-3-0 3-044 N 3-45, TS S T TON O PROTTV RM OVR. 3 05--0 LT 3-004, NOT, 3-050 3 0//00 UPT ST ROM SN,

More information

MATERIAL SEE BOM ANGLES = 2 FINISH N/A

MATERIAL SEE BOM ANGLES = 2 FINISH N/A 9 NOTS:. SSML N NSPT PR SOP 0-9... NSTLL K STKR N X L STKR TO NS O SROU WT TP. 3. PR-PK LNR RNS WT P (XTRM PRSSUR NL R ) RS OR NNRN PPROV QUVLNT. 4. OLOR TT Y T SLS ORR. RRN T MNS OM OR OMPONNTS ONTNN

More information

b.) v d =? Example 2 l = 50 m, D = 1.0 mm, E = 6 V, " = 1.72 #10 $8 % & m, and r = 0.5 % a.) R =? c.) V ab =? a.) R eq =?

b.) v d =? Example 2 l = 50 m, D = 1.0 mm, E = 6 V,  = 1.72 #10 $8 % & m, and r = 0.5 % a.) R =? c.) V ab =? a.) R eq =? xmpl : An 8-gug oppr wr hs nomnl mtr o. mm. Ths wr rrs onstnt urrnt o.67 A to W lmp. Th nsty o r ltrons s 8.5 x 8 ltrons pr u mtr. Fn th mgntu o. th urrnt nsty. th rt vloty xmpl D. mm,.67 A, n N 8.5" 8

More information

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions ulty o Mtmtis Wtrloo, Ontrio N ntr or ution in Mtmtis n omputin r / Mt irls Mr /, 0 rp Tory - Solutions * inits lln qustion. Tr t ollowin wlks on t rp low. or on, stt wtr it is pt? ow o you know? () n

More information

CMPS 2200 Fall Graphs. Carola Wenk. Slides courtesy of Charles Leiserson with changes and additions by Carola Wenk

CMPS 2200 Fall Graphs. Carola Wenk. Slides courtesy of Charles Leiserson with changes and additions by Carola Wenk CMPS 2200 Fll 2017 Grps Crol Wnk Sls ourtsy o Crls Lsrson wt ns n tons y Crol Wnk 10/23/17 CMPS 2200 Intro. to Alortms 1 Grps Dnton. A rt rp (rp) G = (V, E) s n orr pr onsstn o st V o vrts (snulr: vrtx),

More information

COMP 250. Lecture 29. graph traversal. Nov. 15/16, 2017

COMP 250. Lecture 29. graph traversal. Nov. 15/16, 2017 COMP 250 Ltur 29 rp trvrsl Nov. 15/16, 2017 1 Toy Rursv rp trvrsl pt rst Non-rursv rp trvrsl pt rst rt rst 2 Hs up! Tr wr w mstks n t sls or S. 001 or toy s ltur. So you r ollown t ltur rorns n usn ts

More information

Physics 222 Midterm, Form: A

Physics 222 Midterm, Form: A Pysis 222 Mitrm, Form: A Nm: Dt: Hr r som usul onstnts. 1 4πɛ 0 = 9 10 9 Nm 2 /C 2 µ0 4π = 1 10 7 tsl s/c = 1.6 10 19 C Qustions 1 5: A ipol onsistin o two r point-lik prtils wit q = 1 µc, sprt y istn

More information

MAT3707. Tutorial letter 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS. Semester 1. Department of Mathematical Sciences MAT3707/201/1/2017

MAT3707. Tutorial letter 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS. Semester 1. Department of Mathematical Sciences MAT3707/201/1/2017 MAT3707/201/1/2017 Tutoril lttr 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS MAT3707 Smstr 1 Dprtmnt o Mtmtil Sins SOLUTIONS TO ASSIGNMENT 01 BARCODE Din tomorrow. univrsity o sout ri SOLUTIONS TO ASSIGNMENT

More information

DOCUMENT STATUS: MINTP0 E-ST5080, BASE, NO DISPLAY VENDOR: 15.5 INCH MATERIAL SEE BOM FINISH REVISION HISTORY ITEM NO. PART NUMBER DESCRIPTION

DOCUMENT STATUS: MINTP0 E-ST5080, BASE, NO DISPLAY VENDOR: 15.5 INCH MATERIAL SEE BOM FINISH REVISION HISTORY ITEM NO. PART NUMBER DESCRIPTION RV T RVSON STORY SRPTON O Y 0-0-0 PROUTON RLS K. N NOTS:. SRL LL NORMTON: a) VOLTS: V b) MPS:.0 c) YLS: N/ d) WTTS: W e) PS: N/ f) PX #: PX. RTTON LOOS: S / / LN R WT SOPROPYL LOLOL PROR TO PLN.. PK M:

More information

Closed Monochromatic Bishops Tours

Closed Monochromatic Bishops Tours Cos Monoromt Bsops Tours Jo DMo Dprtmnt o Mtmts n Sttsts Knnsw Stt Unvrsty, Knnsw, Gor, 0, USA mo@nnsw.u My, 00 Astrt In ss, t sop s unqu s t s o to sn oor on t n wt or. Ts ms os tour n w t sop vsts vry

More information

EE1000 Project 4 Digital Volt Meter

EE1000 Project 4 Digital Volt Meter Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7-smnt iit tht tlls us wht tht input s

More information

DOCUMENT STATUS: LA-S5302-XXXXS LA, SSS, TRICEPS EXTENSION VERY

DOCUMENT STATUS: LA-S5302-XXXXS LA, SSS, TRICEPS EXTENSION VERY RVSON STORY RV T SRPTON O Y //0 RLS OR PROUTON T LN MR ----- L /0/0 UPT SN N OMPONNTS US: S 3-03 (*N TWO PLS ONLY) WS 3-5, PRT 3-00 TO SSMLY. T OLLOWN UPT: 3-30, 3-403, 3-403, 3-40, 3-45, 3-4, 3-5. 30

More information

Tangram Fractions Overview: Students will analyze standard and nonstandard

Tangram Fractions Overview: Students will analyze standard and nonstandard ACTIVITY 1 Mtrils: Stunt opis o tnrm mstrs trnsprnis o tnrm mstrs sissors PROCEDURE Skills: Dsriin n nmin polyons Stuyin onrun Comprin rtions Tnrm Frtions Ovrviw: Stunts will nlyz stnr n nonstnr tnrms

More information

CSE 332. Data Structures and Parallelism

CSE 332. Data Structures and Parallelism Am Blnk Ltur 20 Wntr 2017 CSE 332 Dt Struturs n Prlllsm CSE 332: Dt Struturs n Prlllsm Grps 1: Wt s Grp? DFS n BFS LnkLsts r to Trs s Trs r to... 1 Wr W v Bn Essntl ADTs: Lsts, Stks, Quus, Prorty Quus,

More information

CSE 332. Graphs 1: What is a Graph? DFS and BFS. Data Abstractions. CSE 332: Data Abstractions. A Graph is a Thingy... 2

CSE 332. Graphs 1: What is a Graph? DFS and BFS. Data Abstractions. CSE 332: Data Abstractions. A Graph is a Thingy... 2 Am Blnk Ltur 19 Summr 2015 CSE 332: Dt Astrtons CSE 332 Grps 1: Wt s Grp? DFS n BFS Dt Astrtons LnkLsts r to Trs s Trs r to... 1 A Grp s Tny... 2 Wr W v Bn Essntl ADTs: Lsts, Stks, Quus, Prorty Quus, Hps,

More information

MINI POST SERIES BALUSTRADE SYSTEM INSTALLATION GUIDE PRODUCT CODE: MPS-RP

MINI POST SERIES BALUSTRADE SYSTEM INSTALLATION GUIDE PRODUCT CODE: MPS-RP MN POST SRS LUSTR SYSTM NSTLLTON U PROUT O: MPS-RP 0 R0 WLL LN 0 RONT LVTON VW R0 N P 0 T RUR LOK LOT ON LSS. SLON SL TYP. OT SS 000 LSS T 0 00 SRS LSS WT 00/00 (0mm NRMNTS VLL) MX. 000 00-0 (ROMMN) 00

More information

OpenMx Matrices and Operators

OpenMx Matrices and Operators OpnMx Mtris n Oprtors Sr Mln Mtris: t uilin loks Mny typs? Dnots r lmnt mxmtrix( typ= Zro", nrow=, nol=, nm="" ) mxmtrix( typ= Unit", nrow=, nol=, nm="" ) mxmtrix( typ= Int", nrow=, nol=, nm="" ) mxmtrix(

More information

Math 166 Week in Review 2 Sections 1.1b, 1.2, 1.3, & 1.4

Math 166 Week in Review 2 Sections 1.1b, 1.2, 1.3, & 1.4 Mt 166 WIR, Sprin 2012, Bnjmin urisp Mt 166 Wk in Rviw 2 Stions 1.1, 1.2, 1.3, & 1.4 1. S t pproprit rions in Vnn irm tt orrspon to o t ollowin sts. () (B ) B () ( ) B B () (B ) B 1 Mt 166 WIR, Sprin 2012,

More information

Complete Solutions for MATH 3012 Quiz 2, October 25, 2011, WTT

Complete Solutions for MATH 3012 Quiz 2, October 25, 2011, WTT Complt Solutions or MATH 012 Quiz 2, Otor 25, 2011, WTT Not. T nswrs ivn r r mor omplt tn is xpt on n tul xm. It is intn tt t mor omprnsiv solutions prsnt r will vlul to stunts in stuyin or t inl xm. In

More information

ELECTRONIC SUPPLEMENTARY INFORMATION

ELECTRONIC SUPPLEMENTARY INFORMATION Elctronc Supplmntry Mtrl (ESI) or Polymr Cmstry. Ts ournl s T Royl Socty o Cmstry 2015 ELECTRONIC SUPPLEMENTARY INFORMATION Poly(lyln tcont)s An ntrstn clss o polystrs wt proclly loct xo-cn oul ons suscptl

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h

More information

Face Detection and Recognition. Linear Algebra and Face Recognition. Face Recognition. Face Recognition. Dimension reduction

Face Detection and Recognition. Linear Algebra and Face Recognition. Face Recognition. Face Recognition. Dimension reduction F Dtto Roto Lr Alr F Roto C Y I Ursty O solto: tto o l trs s s ys os ot. Dlt to t to ltpl ws. F Roto Aotr ppro: ort y rry s tor o so E.. 56 56 > pot 6556- stol sp A st o s t ps to ollto o pots ts sp. F

More information

Strongly connected components. Finding strongly-connected components

Strongly connected components. Finding strongly-connected components Stronly onnt omponnts Fnn stronly-onnt omponnts Tylr Moor stronly onnt omponnt s t mxml sust o rp wt rt pt twn ny two vrts SE 3353, SMU, Dlls, TX Ltur 9 Som sls rt y or pt rom Dr. Kvn Wyn. For mor normton

More information

BASIC CAGE DETAILS SHOWN 3D MODEL: PSM ASY INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY SPRING FINGERS CLOSED TOP

BASIC CAGE DETAILS SHOWN 3D MODEL: PSM ASY INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY SPRING FINGERS CLOSED TOP MO: PSM SY SI TIS SOWN SPRIN INRS OS TOP INNR W TS R OIN OVR S N OVR OR RIIITY. R TURS US WIT OPTION T SINS. R (UNOMPRSS) RR S OPTION (S T ON ST ) IMNSIONS O INNR SIN TO UNTION WIT QU SM ORM-TOR (zqsp+)

More information

Minimum Spanning Trees (CLRS 23)

Minimum Spanning Trees (CLRS 23) Mnmum Spnnn Trs (CLRS 3) T prolm Rll t nton o spnnn tr: Gvn onnt, unrt rp G = (V, E), sust o s o G su tt ty onnt ll vrts n G n orm no yls s ll spnnn tr (ST) o G. Any unrt, onnt rp s spnnn tr. Atully, rp

More information

CS 103 BFS Alorithm. Mark Redekopp

CS 103 BFS Alorithm. Mark Redekopp CS 3 BFS Aloritm Mrk Rkopp Brt-First Sr (BFS) HIGHLIGHTED ALGORITHM 3 Pt Plnnin W'v sn BFS in t ontxt o inin t sortst pt trou mz? S?? 4 Pt Plnnin W xplor t 4 niors s on irtion 3 3 3 S 3 3 3 3 3 F I you

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

Present state Next state Q + M N

Present state Next state Q + M N Qustion 1. An M-N lip-lop works s ollows: I MN=00, th nxt stt o th lip lop is 0. I MN=01, th nxt stt o th lip-lop is th sm s th prsnt stt I MN=10, th nxt stt o th lip-lop is th omplmnt o th prsnt stt I

More information

TCI SERIES, 3 CELL THE COOLING TOWER CO., L.C. TCI 3 CELL SERIES GA

TCI SERIES, 3 CELL THE COOLING TOWER CO., L.C. TCI 3 CELL SERIES GA of T SIN IS T PROPRTY O T OOLIN TOWR OMPNY, L, N IS LON OR MUTUL SSISTN. IT IS NOT TO ORWR NOR RPRINT IN NY ORM WITOUT WRITTN PRMISSION. L W OPTIONL SS PLTORM " x " STNR PLTORM PR LL OPTIONL VIRTION SWIT

More information

DOCUMENT STATUS: CORE HEALTH & FITNESS, LLC IL-D2002-XXAAX IP,DUAL ADJUSTIBLE PULLEY MATERIAL SEE BOM FINISH N/A N/A SHEET SIZE: B SCALE: 1:33.

DOCUMENT STATUS: CORE HEALTH & FITNESS, LLC IL-D2002-XXAAX IP,DUAL ADJUSTIBLE PULLEY MATERIAL SEE BOM FINISH N/A N/A SHEET SIZE: B SCALE: 1:33. NOTS: RVSON STORY RV T SRPTON O Y //04 RLS OR PROUTON 433 P 34 55 033 OUMNT STTUS: NOT O PROPRTRY NORMTON TS OUMNT SLL NOT RPROU NOR SLL T NORMTON ONTN RN US Y OR SLOS TO OTR XPT S XPRSSLY UTORZ Y OR LT

More information

Decimals DECIMALS.

Decimals DECIMALS. Dimls DECIMALS www.mthltis.o.uk ow os it work? Solutions Dimls P qustions Pl vlu o imls 0 000 00 000 0 000 00 0 000 00 0 000 00 0 000 tnths or 0 thousnths or 000 hunrths or 00 hunrths or 00 0 tn thousnths

More information

Planar convex hulls (I)

Planar convex hulls (I) Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

BASIC CAGE DETAILS D C SHOWN CLOSED TOP SPRING FINGERS INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY

BASIC CAGE DETAILS D C SHOWN CLOSED TOP SPRING FINGERS INNER WALL TABS ARE COINED OVER BASE AND COVER FOR RIGIDITY SI TIS SOWN OS TOP SPRIN INRS INNR W TS R OIN OVR S N OVR OR RIIITY. R IMNSIONS O INNR SIN TO UNTION WIT QU SM ORM-TOR (zqsp+) TRNSIVR. R. RR S OPTION (S T ON ST ) TURS US WIT OPTION T SINS. R (INSI TO

More information

QUESTIONS BEGIN HERE!

QUESTIONS BEGIN HERE! Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt o Computr n Inormtion Sins CSCI 2710 (Trno) Disrt Struturs TEST or Sprin Smstr, 2005 R this or strtin! This tst is los ook

More information

QUESTIONS BEGIN HERE!

QUESTIONS BEGIN HERE! Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt of Computr n Informtion Sins CSCI 710 (Trnoff) Disrt Struturs TEST for Fll Smstr, 00 R this for strtin! This tst is los ook

More information

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1 Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):

More information

Cycles and Simple Cycles. Paths and Simple Paths. Trees. Problem: There is No Completely Standard Terminology!

Cycles and Simple Cycles. Paths and Simple Paths. Trees. Problem: There is No Completely Standard Terminology! Outlin Computr Sin 331, Spnnin, n Surphs Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #30 1 Introution 2 3 Dinition 4 Spnnin 5 6 Mik Joson (Univrsity o Clry) Computr Sin 331 Ltur #30 1 / 20 Mik

More information

Graphs Depth First Search

Graphs Depth First Search Grp Dpt Frt Sr SFO 337 LAX 1843 1743 1233 802 DFW ORD - 1 - Grp Sr Aort - 2 - Outo Ø By unrtnn t tur, you ou to: q L rp orn to t orr n w vrt r ovr, xpor ro n n n pt-rt r. q Cy o t pt-rt r tr,, orwr n ro

More information

L.3922 M.C. L.3922 M.C. L.2996 M.C. L.3909 M.C. L.5632 M.C. L M.C. L.5632 M.C. L M.C. DRIVE STAR NORTH STAR NORTH NORTH DRIVE

L.3922 M.C. L.3922 M.C. L.2996 M.C. L.3909 M.C. L.5632 M.C. L M.C. L.5632 M.C. L M.C. DRIVE STAR NORTH STAR NORTH NORTH DRIVE N URY T NORTON PROV N RRONOUS NORTON NVRTNTY PROV. SPY S NY TY OR UT T TY RY OS NOT URNT T S TT T NORTON PROV S ORRT, NSR S POSS, VRY ORT S N ON N T S T TY RY. TS NORTON S N OP RO RORS RT SU "" YW No.

More information

Lecture II: Minimium Spanning Tree Algorithms

Lecture II: Minimium Spanning Tree Algorithms Ltur II: Mnmum Spnnn Tr Alortms Dr Krn T. Hrly Dprtmnt o Computr Sn Unvrsty Coll Cork Aprl 0 KH (/0/) Ltur II: Mnmum Spnnn Tr Alortms Aprl 0 / 5 Mnmum Spnnn Trs Mnmum Spnnn Trs Spnnn Tr tr orm rom rp s

More information

Graph Search (6A) Young Won Lim 5/18/18

Graph Search (6A) Young Won Lim 5/18/18 Grp Sr (6A) Youn Won Lm Copyrt () 2015 2018 Youn W. Lm. Prmon rnt to opy, trut n/or moy t oumnt unr t trm o t GNU Fr Doumntton Ln, Vron 1.2 or ny ltr vron pul y t Fr Sotwr Founton; wt no Invrnt Ston, no

More information

PRECAST APPROACH SLAB NOTES

PRECAST APPROACH SLAB NOTES ULNS TS ULN RWNS RPRSNT TYPL TLS OR T SN N TLN O PRST PPRO SLS. TS STS R NLU TO PROV N XMPL O T RTN LYOUT O TYPL PRST PPRO SL. TWO RNT PPRO SL SYSTMS R SOWN: SUR PPRO SLS: SLS TT R PL WT T TOP SUR T OR

More information

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This

More information

Applications of trees

Applications of trees Trs Apptons o trs Orgnzton rts Attk trs to syst Anyss o tr ntworks Prsng xprssons Trs (rtrv o norton) Don-n strutur Mutstng Dstnton-s orwrng Trnsprnt swts Forwrng ts o prxs t routrs Struturs or nt pntton

More information

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy. LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL

More information

Aquauno Video 6 Plus Page 1

Aquauno Video 6 Plus Page 1 Connt th timr to th tp. Aquuno Vio 6 Plus Pg 1 Usr mnul 3 lik! For Aquuno Vio 6 (p/n): 8456 For Aquuno Vio 6 Plus (p/n): 8413 Opn th timr unit y prssing th two uttons on th sis, n fit 9V lklin ttry. Whn

More information

Designing A Concrete Arch Bridge

Designing A Concrete Arch Bridge This is th mous Shwnh ri in Switzrln, sin y Rort Millrt in 1933. It spns 37.4 mtrs (122 t) n ws sin usin th sm rphil mths tht will monstrt in this lsson. To pro with this lsson, lik on th Nxt utton hr

More information

Dental PBRN Study: Reasons for replacement or repair of dental restorations

Dental PBRN Study: Reasons for replacement or repair of dental restorations Dntl PBRN Stuy: Rsons or rplmnt or rpr o ntl rstortons Us ts Dt Collton Form wnvr stuy rstorton s rpl or rpr. For nrollmnt n t ollton you my rpl or rpr up to 4 rstortons, on t sm ptnt, urn snl vst. You

More information

Priority Search Trees - Part I

Priority Search Trees - Part I .S. 252 Pro. Rorto Taassa oputatoal otry S., 1992 1993 Ltur 9 at: ar 8, 1993 Sr: a Q ol aro Prorty Sar Trs - Part 1 trouto t last ltur, w loo at trval trs. or trval pot losur prols, ty us lar spa a optal

More information

B ADDED BADGE PN , CHANGED TO C SIZE FOR ASSY, ADDED NOTES DN J DETAIL A SCALE 1 : INCH MATERIAL

B ADDED BADGE PN , CHANGED TO C SIZE FOR ASSY, ADDED NOTES DN J DETAIL A SCALE 1 : INCH MATERIAL 0 RVSONS RV. T SRPTON O Y 0--0 PROUTON RLS N 0--0 PN 00-0, N TO SZ OR SSY, NOTS N TL SL :. N TM NO. PRT NUMR SRPTON QTY. NOT 00-0, PROUT, P-ST 0 NOTS:. SRL LL NORMTON: a) VOLTS: V b) MPS:.0 c) YLS: N/

More information

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o

More information

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1 CSC 00 Disrt Struturs : Introuon to Grph Thory Grphs Grphs CSC 00 Disrt Struturs Villnov Univrsity Grphs r isrt struturs onsisng o vrs n gs tht onnt ths vrs. Grphs n us to mol: omputr systms/ntworks mthml

More information

16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am

16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am 16.unii Introution to Computrs n Prormmin SOLUTIONS to Exmintion /30/0 9:05m - 10:00m Pro. I. Kristin Lunqvist Sprin 00 Grin Stion: Qustion 1 (5) Qustion (15) Qustion 3 (10) Qustion (35) Qustion 5 (10)

More information

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim MULTIPLE STITCHES Nrtiti Ehos o Rgl omponnts vok visions o th pst sign y Hln Tng-Lim Us vrity o stiths to rt this rgl yt wrl sign. Prt sping llows squr s to mk roun omponnts tht rp utiully. FCT-SC-030617-07

More information

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht

More information

RMMP Vianu 2013 Problema 1

RMMP Vianu 2013 Problema 1 RMMP Vnu Probl Dl DAVIDSCU Arn DAFINI sk. Knt nrgy o t r. Soluton Fgur Clulul ontulu nrţ nsty o wl trl ( t lngt o wl s ) s ( ) Consrng t lntry prs ng t ss y t lntry wt rspt o wl s s y r J ( ) wt y r (

More information

D t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d

More information

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari Grphs CSC 1300 Disrt Struturs Villnov Univrsity Grphs Grphs r isrt struturs onsis?ng of vr?s n gs tht onnt ths vr?s. Grphs n us to mol: omputr systms/ntworks mthm?l rl?ons logi iruit lyout jos/prosss f

More information

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms rp loritms lrnin ojtivs loritms your sotwr systm sotwr rwr lrn wt rps r in mtmtil trms lrn ow to rprsnt rps in omputrs lrn out typil rp loritms wy rps? intuitivly, rp is orm y vrtis n s twn vrtis rps r

More information

Functions and Graphs 1. (a) (b) (c) (f) (e) (d) 2. (a) (b) (c) (d)

Functions and Graphs 1. (a) (b) (c) (f) (e) (d) 2. (a) (b) (c) (d) Functions nd Grps. () () (c) - - - O - - - O - - - O - - - - (d) () (f) - - O - 7 6 - - O - -7-6 - - - - - O. () () (c) (d) - - - O - O - O - - O - -. () G() f() + f( ), G(-) f( ) + f(), G() G( ) nd G()

More information

A general N-dimensional vector consists of N values. They can be arranged as a column or a row and can be real or complex.

A general N-dimensional vector consists of N values. They can be arranged as a column or a row and can be real or complex. Lnr lgr Vctors gnrl -dmnsonl ctor conssts of lus h cn rrngd s column or row nd cn rl or compl Rcll -dmnsonl ctor cn rprsnt poston, loct, or cclrton Lt & k,, unt ctors long,, & rspctl nd lt k h th componnts

More information

S i m p l i f y i n g A l g e b r a SIMPLIFYING ALGEBRA.

S i m p l i f y i n g A l g e b r a SIMPLIFYING ALGEBRA. S i m p l i y i n g A l g r SIMPLIFYING ALGEBRA www.mthltis.o.nz Simpliying SIMPLIFYING Algr ALGEBRA Algr is mthmtis with mor thn just numrs. Numrs hv ix vlu, ut lgr introus vrils whos vlus n hng. Ths

More information

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion

More information

The R-Tree. Yufei Tao. ITEE University of Queensland. INFS4205/7205, Uni of Queensland

The R-Tree. Yufei Tao. ITEE University of Queensland. INFS4205/7205, Uni of Queensland Yu To ITEE Unvrsty o Qunsln W wll stuy nw strutur ll t R-tr, w n tout o s mult-mnsonl xtnson o t B-tr. T R-tr supports ntly vrty o qurs (s w wll n out ltr n t ours), n s mplmnt n numrous ts systms. Our

More information

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,

More information

l f t n nd bj t nd x f r t l n nd rr n n th b nd p phl t f l br r. D, lv l, 8. h r t,., 8 6. http://hdl.handle.net/2027/miun.aey7382.0001.001 P bl D n http://www.hathitrust.org/access_use#pd Th r n th

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

Binomials and Pascal s Triangle

Binomials and Pascal s Triangle Binomils n Psl s Tringl Binomils n Psl s Tringl Curriulum R AC: 0, 0, 08 ACS: 00 www.mthltis.om Binomils n Psl s Tringl Bsis 0. Intif th prts of th polnomil: 8. (i) Th gr. Th gr is. (Sin is th highst

More information

NOTE: ONLY RIGHT IDLER (CONFIGURATION A) ARM SHOWN IN VIEWS ON THIS PAGE

NOTE: ONLY RIGHT IDLER (CONFIGURATION A) ARM SHOWN IN VIEWS ON THIS PAGE 0 PP PP PP PP PP PP NOT: ONLY RIT ILR (ONIURTION ) RM SOWN IN VIWS ON TIS P ITM SRIPTION MTRIL QTY. IL RM - RIT / RIL LIN TUIN / O (0.0 WLL) ISI RT 0 ROMOLY LINR INS IL RM - LT / RIL LIN TUIN / O (0.0

More information

Self-Adjusting Top Trees

Self-Adjusting Top Trees Th Polm Sl-jsting Top Ts ynmi ts: ol: mintin n n-tx ost tht hngs o tim. link(,w): ts n g twn tis n w. t(,w): lts g (,w). pplition-spii t ssoit with gs n/o tis. ont xmpls: in minimm-wight g in th pth twn

More information

F102 1/4 AMP +240 VDC SEE FIGURE 5-14 FILAMENT AND OVEN CKTS BLU J811 BREAK-IN TB103 TO S103 TRANSMITTER ASSOCIATED CAL OFF FUNCTION NOTE 2 STANDBY

F102 1/4 AMP +240 VDC SEE FIGURE 5-14 FILAMENT AND OVEN CKTS BLU J811 BREAK-IN TB103 TO S103 TRANSMITTER ASSOCIATED CAL OFF FUNCTION NOTE 2 STANDBY OWR OR F0 M NOT S0 RT OF FUNTI FL0 T0 OWR SULY SUSSIS T0 T0 WIR FOR 0 V OWR SULY SUSSIS T0 WIR FOR V 0 0 RT V0 RT V0. V RT V0 RT V0 NOT. V. V NOT +0 V 0 +0 V. V 0 FUNTI NOT L +0 V S FIUR - FILMNT N OVN

More information

Chem 104A, Fall 2016, Midterm 1 Key

Chem 104A, Fall 2016, Midterm 1 Key hm 104A, ll 2016, Mitrm 1 Ky 1) onstruct microstt tl for p 4 configurtion. Pls numrt th ms n ml for ch lctron in ch microstt in th tl. (Us th formt ml m s. Tht is spin -½ lctron in n s oritl woul writtn

More information

CSE 332. Graphs 1: What is a Graph? DFS and BFS. Data Abstractions. CSE 332: Data Abstractions. A Graph is a Thingy... 2

CSE 332. Graphs 1: What is a Graph? DFS and BFS. Data Abstractions. CSE 332: Data Abstractions. A Graph is a Thingy... 2 Am Blnk Ltur 0 Autumn 0 CSE 33: Dt Astrtons CSE 33 Grps : Wt s Grp? DFS n BFS Dt Astrtons LnkLsts r to Trs s Trs r to... A Grp s Tny... Wr W v Bn Essntl ADTs: Lsts, Stks, Quus, Prorty Quus, Hps, Vnll Trs,

More information

Problem solving by search

Problem solving by search Prolm solving y srh Tomáš voo Dprtmnt o Cyrntis, Vision or Roots n Autonomous ystms Mrh 5, 208 / 3 Outlin rh prolm. tt sp grphs. rh trs. trtgis, whih tr rnhs to hoos? trtgy/algorithm proprtis? Progrmming

More information

MATERIAL SEE BOM ANGLES = 2 > 2000 DATE MEDIUM FINISH

MATERIAL SEE BOM ANGLES = 2 > 2000 DATE MEDIUM FINISH NOTS:. LN MTN SUR WT NTUR/SOPROPYL LOOL PROR TO RN L OR LOO. PPLY LOTT 4 ON TRS. TORQU TO. Nm / 00 lb-in 4. TORQU TO 45-50 Nm / - lb-ft 5. TORQU TO Nm / 4.5 lb-ft. TORQU TO 0 Nm / lb-in. TORQU TO 5.5 Nm

More information

Instructions for Section 1

Instructions for Section 1 Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks

More information

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem)

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem) 12/3/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 Ciruits Cyl 2 Eulr

More information

CHELOURANYAN CALENDAR FOR YEAR 3335 YEAR OF SAI RHAVË

CHELOURANYAN CALENDAR FOR YEAR 3335 YEAR OF SAI RHAVË CHELOURANYAN CALENDAR FOR YEAR YEAR OF SAI RHAVË I tou woust n unon wt our Motr, now tt tou st nvr t Hr. I tou woust sp t v o mttr, now tt tr s no mttr n no v. ~Cry Mry KEY TO CALENDAR T Dys o t W In t

More information

VLSI Testing Assignment 2

VLSI Testing Assignment 2 1. 5-vlu D-clculus trut tbl or t XOR unction: XOR 0 1 X D ~D 0 0 1 X D ~D 1 1 0 X ~D D X X X X X X D D ~D X 0 1 ~D ~D D X 1 0 Tbl 1: 5-vlu D-clculus Trut Tbl or t XOR Function Sinc 2-input XOR t wors s

More information

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs Prt 10. Grphs CS 200 Algorithms n Dt Struturs 1 Introution Trminology Implmnting Grphs Outlin Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 2 Ciruits Cyl A spil yl

More information