03 - ;LEX EVI XLI X[S TVMQEV HM’IVIRGIW FIX[IIR 1&...

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Unformatted text preview: ;LEX EVI XLI X[S TVMQEV] HM’IVIRGIW FIX[IIR 1%80%& WGVMTXW ERH JYRGXMSRW# *YRGXMSR “PIW GSQTEVIH XS WGVMTX “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“PIW GER VIXYVR QSVI XLIR VIWYPX *YRGXMSRW GER EGGITX MRTYXW ERH SYXTYXW 7GVMTXW GERRSX % WGVMTX WMQTP] WEZIW E WIVMIW SJ 1EXPEF GSQQERHW XLEX GER FI EGGIWWIH EX ER] XMQI ;LIVI EW E JYRGXMSR GER EGGITX MRTYX EVKYQIRXW ERH VIXYVR SYXTYXW 3XLIV HM’IVIRGIW EVI XLEX XLI ZEVMEFPIW MR E WGVMTX EVI VIXEMRIH IZIR EJXIV XLI WGVMTX MW I\IGYXIH [LIVI EW XLI ZEVMEFPIW MR E JYRGXMSR EVI PSGEP ERH EVI IVEWIH EJXIV XLI JYRGXMSR MW I\IGYXIH % WGVMTX “PI MW E WIVMIW SJ 1%80%& GSQQERHW XLEX EVI WEZIH SR E “PI *YRGXMSR “PIW EVI 1 “PIW XLEX WXEVX [MXL XLI [SVH JYRGXMSR 7GVMTXW WXSVI XLI RYQIVMGEP HEXE [LMPI JYRGXMSRW XEOI YWIV MRTYX 7IGSRHP] JYRGXMSRW GER FI VIYWIH :EKYI RIIHW XS FI QSVI TVIGMWI ?&SXL JYRGXMSRW ERH WGVMTXW GER FI VIYWIHA ZEVMEFPIW MR E JYRGXMSR EVI IVEWIH EJXIV XLI JYRGXMSR MW I\IGYXIH MR JYRGXMSR [LIVI XLI ZEVMEFPIW MR WGVMTX WXMPP LSPH E ZEPYI EJXIV I\IGYXIH *YRGXMSRW GER VIXYVR QSVI XLER SRI VIWYPX %RW[IV MR TEVX MW SOE] FYX GSYPH FI QSVI TVIGMWI %RW[IV MR TEVX MW RSX WY•GMIRXP] TVIGMWI JYRGXMSRW GER VIXYVR ^IVS VIWYPXW EW [IPP XLIVI MW EPWS XLI QEXXIV SJ MRTYXW ERH WTIGMJ]MRK XLI HM’IVIRGI VIPEXMZI XS WGVMTXW *YRGXMSRW EPPS[ YW XS MRTYX HEXE MR VIEP XMQI [LIVIEW WGVMTXW HS RSX %PWS *YRGXMSRW GER VIXYVR SYXTYXW FEWIH SR XLI MRTYXW [LMPI WGVMTXW GER X 6IEP XMQI MW RSX VIEPP] ETTVSTVMEXI MR XLMW GSRXI\X - GERRSX UYMXI YRHIVWXERH [LEX XLI WXYHIRX QIERW XS WE] 8LI WIGSRH WIRXIRGI MW QSVI SV PIWW GSVVIGX ;LEX EVI XLI X[S TVMQEV] HM’IVIRGIW FIX[IIR 1%80%& WGVMTXW ERH JYRGXMSRW# 1] VIWTSRWI 7GVMTX “PIW [LIR I\IGYXIH LEZI EGGIWW XS ZEVMEFPIW MR XLI KPSFEP 1%80%& [SVOWTEGI %W WYGL GLERKIW QEHI XS ZEVMEFPIW [LIR I\IGYXMRK E WGVMTX GLERKI XLI HEXE MR XLI KPSFEP [SVOWTEGI &] GSRXVEWX JYRGXMSRW [LIR I\IGYXIH GERRSX EGGIWW ZEVMEFPIW MR XLI KPSFEP [SVOWTEGI -RWXIEH ZEVMEFPIW GVIEXIH [MXLMR JYRGXMSRW EVI WXVMGXP] PSGEP ZEVMEFPIW ERH HEXE JVSQ XLI KPSFEP [SVOWTEGI GER SRP] FI TEWWIH MRXS E JYRGXMSR YWMRK MRTYX ZEVMEFPIW *YRGXMSRW QE] YWI ^IVS SV QSVI MRTYX ZEVMEFPIW ERH ^IVS SV QSVI SYXTYX ZEVMEFPIW [LIR MRZSOIH 7GVMTXW GERRSX FI MRZSOIH [MXL MRTYX ERH SYXTYX ZEVMEFPIW %W I\TPEMRIH SR T ZIGXSVMWEXMSR EPPS[W JSVQYPEW XS FI ETTPMIH XS EVVE]W SJ HEXE ZIGXSVW SV QEXVMGIW [MXLSYX JSV PSSTW EW MR XVEHMXMSREP TVSKVEQQMRK PERKYEKIW )\TPEMR [L] XLIVI EVI ZIGXSVMWIH ZIVWMSRW SJ XLI STIVEXSVW B ERH REQIP] B ERH VIWTIGXMZIP] FYX XLIVI EVI RS GSQTEVEFPI ZIVWMSRW SJ XLI STIVEXSVW ERH M I XLIVI MW RS RIIH XS LEZI SV 8LI HSX STIVEXSV MW YWIH WS XLEX EVVE] GEPGYPEXMSRW EVI GEVVMIH SYX IPIQIRX F] IPIQIRX ,S[IZIV [LIR EHHMRK SV WYFXVEGXMRK XLIVI VIEPP] MW RS RIIH XS WTIGMJ] XLEX GEPGYPEXMSRW RIIH XS FI GEVVMIH SYX IPIQIRX F] IPIQIRX 8LIVI MW RS RIIH XS LEZI ERH STIVEXSVW XLEX EVI ZIGXSVM^IH FIGEYWI XLIWI JYRGXMSRW EVI EPVIEH] IRXV] F] IRXV] STIVEXSVW 8LMW QIERW XLEX IZIV] TSWMXMSR MR SRI EVVE] [MPP FI STIVEXIH YTSR YWMRK XLI SV STIVEXSV [LIR X[S EVVE]W SJ IUYEP WM^I EVI EHHIH SV WYFXVEGXIH 8LMW MW RSX XVYI JSV STIVEXSVW WYGL EW QYPXMTPMGEXMSR FIGEYWI WYGL JYRGXMSRW EW ZIGXSV QYPXMTPMGEXMSR I\MWX ?8LMW UYIWXMSR SFZMSYWP] GEYWIW QSVI GSRJYWMSR A 1] ERW[IV 8LIVI MW RS RIIH XS LEZI ZIGXSVMWIH ZIVWMSRW SJ XLI STIVEXSV ERH FIGEYWI MR WXERHEVH PMRIEV EPKIFVE RSXEXMSR JSV QEXVMGIW SJ XLI WEQI HMQIRWMSRW EHHMXMSR ERH WYFXVEGXMSR MW HI“RIH IPIQIRX[MWI &] GSRXVEWX [I RIIH XS WTIGMJ] IPIQIRX[MWI QYPXMTPMGEXMSR HMZMWMSR ERH I\TSRIRXMEXMSR I\TPMGMXP] XS GSRXVEWX FIX[IIR QEXVM\ QYPXMTPMGEXMSR ERH WMQMPEV STIVEXMSRW HIVMZIH YWMRK QEXVM\ TVSHYGXW I K QEXVM\ I\TSRIRXMEXMSR JSV WUYEVI QEXVMGIW QYPXMTPMGEXMSR F] E QEXVM\ MRZIVWI IXG -R WLSVX [I RIIH XLI HSX XS HMWXMRKYMWL % & JVSQ % & 3R XLI SXLIV LERH XLIVI MW SRP] SRI TSWWMFPI WIRWMFPI MRXIVTVIXEXMSR SJ % & SV % & ,S[ HS - ORS[ [LIR XS YWI ZIGXSVMWIH ZIVWMSRW SJ STIVEXSVW MR 1%80%&# %RW[IV XLI UYIWXMSR ]SY RIIH XS EWO [LIR PSSOMRK EX E JSVQYPE MW [LEX OMRH SJ HEXE EVI XLI ZEVMEFPIW MR XLI JSVQYPE M I EVI XLI] WGEPEV ZEPYIW SV EVI XLI] EVVE]W# S FSXL ZEVMEFPIW EVI WGEPEVW ]SY HS RSX RIIH XLI HSX STIVEXSVW EX EPP S SRI ZEVMEFPI MW E WGEPEV XLI SXLIV MW ER EVVE] ]SY TVSFEFP] HSR X RIIH XLI HSX STIVEXSVW YRPIWW ]SY RIIH XS I\TPMGMXP] JSVGI ER IPIQIRX[MWI STIVEXMSR EW STTSWIH XS SRI FEWIH SR QEXVM\ FEWIH TVSHYGXW S FSXL ZEVMEFPIW EVI EVVE]W ]SY RIIH XS GLIGO XLEX XLI STIVEXMSR ]SY [ERX MW QIERX XS FI ETTPMIH IPIQIRX[MWI SV YWMRK QEXVM\ TVSHYGX HI“RMXMSRW "" ;LIR EPP ZEVMEFPIW EVI WGEPEVW HSXW EVI VIHYRHERX "" WGEPEV ! "" WGEPEV ! "" WGEPEV WGEPEV 8LMW MW 3/ ERW ! "" WGEPEV ERW ! WGEPEV 8LMW MW 3/ "" WGEPEV ERW ! WGEPEV 8LMW MW 3/ "" WGEPEV ERW ! WGEPEV 8LMW MW 3/ "" WGEPEV B WGEPEV ERW ! 8LMW MW 3/ ;LIR [I QM\ WGEPEVW ERH EVVE]W HM’IVIRX VIWYPXW GER SGGYV "" EVVE] ! ? A EVVE] ! "" EVVE] ERW ! WGEPEV 8LMW MW 3/ YWIW WGEPEV I\TERWMSR "" EVVE] ERW ! WGEPEV 8LMW MW 3/ YWIW WGEPEV I\TERWMSR "" EVVE] ERW ! WGEPEV 8LMW MW 3/ YWIW WGEPEV I\TERWMSR "" EVVE] ERW ! WGEPEV 8LMW MW 3/ YWIW WGEPEV I\TERWMSR "" EVVE] B WGEPEV ERW ! 8LMW YWIW QEXVM\ MRXIVTVIXEXMSR M M M M WGEPEV EVVE] 7LSYPH KMZI W]RXE\ IVVSV ### )VVSV YWMRK !!" QPHMZMHI 1EXVM\ HMQIRWMSRW QYWX EKVII "" EVVE] ! ? EVVE] ! "" EVVE] ! ? EVVE] ! A A "" ;LIR [I GSQFMRI EVVE]W [I RIIH HSX EVMXLQIXMG XS HMWXMRKYMWL "" IPIQIRX[MWI GSQTYXEXMSRW JVSQ SRIW YWMRK QEXVM\ QYPXMTPMGEXMSR "" EVVE] EVVE] XLMW MW 3/ ERW ! "" EVVE] ERW ! EVVE] XLMW MW 3/ "" EVVE] ERW ! EVVE] XLMW YWIW QEXVM\ QEXVM\ TVSHYGXW "" EVVE] ERW ! EVVE] XLMW YWIW IPIQIRX[MWI TVSHYGXW "" EVVE] ERW ! EVVE] XLMW YWIW IPIQIRX[MWI HMZMWMSR "" EVVE] ERW ! "" EVVE] ERW ! EVVE] B EVVE] KMZIW EVVE] EVVE] B "" EVVE] BEVVE] ### )VVSV YWMRK !!" QTS[IV -RTYXW QYWX FI E WGEPEV ERH E WUYEVI QEXVM\ "" EVVE] B ERW ! "" ? AB ### )VVSV YWMRK !!" QTS[IV -RTYXW QYWX FI E WGEPEV ERH E WUYEVI QEXVM\ Solution MATH 2070 In-class Assignment Jan. 17, 2011 Student Number: Student Number: Student Number: 1. Consider the following Matlab commands A1 A2 B1 B2 C1 C2 = = = = = = [ 1, 3; -2, 4]; [ 1, 3; 2, 4]; A1 * A1; A1 .* A1; A2^2; A2.^2; 1EXVM\ QEXVM\ TVSHYGX )PIQIRX[MWI TVSHYGX )\TSRIRXMEXMSR SJ WUYEVI QEXVM\ )PIQIRX[MWI I\TSRIRXMEXMSR Indicate which of the following statements are true or false. (a) The matrix B1 is identical to the matrix B2. (a) *EPWI (b) The matrix B1 is identical to the matrix C1. (b) *EPWI (c) *EPWI (c) The matrix C1 is identical to the matrix C2. (d) The matrix C1 is identical to the matrix B2. 1EXVM\ WUYEVI VSSX (e) The matrix sqrtm(B1) is identical to the matrix A1. 1EXVM\ WUYEVI VSSX (d) (e) *EPWI 8VYI (f) The matrix sqrtm(B2) is identical to the matrix A2. (f) *EPWI (g) *EPWI (h) 8VYI (g) The matrix sqrt(C1) is identical to the matrix A1. (h) The matrix sqrt(C2) is identical to the matrix A2. 2. Write in the space below the body of a function m-file gravityforce.m that computes the gravitational force acting on a body of mass m (in kg) at height h (in m) above the ground as determined by Newton’s law of Universal Gravitation. Recall, according to Newton’s theory, the gravitational force experienced by two bodies is proportional to the mass of each and inversely proportional to the square of the distance between the two. For a body at height h above the ground, then, this would be GME m , F= (RE + h)2 where ME = 5.9742 × 1024 kg, RE = 6.3781 × 103 km is the radius of the earth, and G = 6.67300 × 10−11 m3 kg−1 s−2 . Your function should accept two input arguments, h and m and return the corresponding value of F . function F = gravityforce( h, m ) G = 6.67300e-11; % Constant of gravitation M_E = 5.9742e24; % Mass of Earth R_E = 6.3781e6 ; % Radius of Earth F = G*m*M_E / (R_E+h)^2; end function F = gravityforce( h, m ) %GRAVITYFORCE Computes force of gravity % Input: % h = height (m) % m = mass (kg) % Output: % F = Gravitational force (N) G= M_E R_E F= end 6.67300e-11; % Constant of gravitation = 5.9742e24; % Mass of Earth = 6.3781e6 ; % Radius of Earth G*m*M_E ./ (R_E+h).^2; ...
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This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.

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