What is the relative velocity (in meters per second) between an observer on earth and a galaxy where the H-beta line of Hydrogen is measured to be 622 nm? (The wavelength of the H-beta line as measured at rest in the laboratory is 486 nm.)3.How fast is the typical oxygen molecule (with a mass of 5.31e-26 kg) traveling when it is at a temperature of 440 Kelvins?4.Suppose you wish to measure the mass of a planet. To do so, you place a test mass in orbit around the planet at a distance of 6.6e+8 meters from the center of the planet. You find that the orbital period is 2.1e+5 seconds. What is the mass of the planet?

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Is the U.S. dollar strong or weak in international foreign exchange markets?

What is a “foreign exchange rate”?

What is the current U.S. dollar foreign exchange rate relative to major trading countries’ currencies?

Choose a foreign country’s currency and determine if the U.S. dollar is getting stronger (appreciating) or weaker (depreciating)? Explain this trend using textbook theory and business journalists’ explanations.

How do these trends impact various social and economic groups within our country?

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Need to find basis for orthagonal complement of th a following sub spaces(4.4.13)

is the zero function f ( 20 )But the orthogonal complemand so ( ( P (0 ) ) ) = C / a , 6 ) * P ( )plement of fo istandbeganThe difference is that in infinite- dimensional function( of in the eatingcan be better hereas it finite dimensions every prove Will proper lywho led Are )( 2 ) Write downbecubies ous an infinitesimal fraction of the entire vector space is a fourthparadox is interestingly , the reason behind the success of numeric Howard !to the orthogonalsuch as the finite element method , ( 81FOXin function space120 Let WC Vthe Let beanProve thatExercises272 Prove that isthen wit WitNote : In Exercises 4 4 . 12 – 15 , use the dot product .123 1 3 ) Show the4 . 4 . 12 . Find the orthogonal complement WV of the subsindicated vectors . What is the dimension of W in each case ?subspaces VCR spanned by thelines in !( ( ) ( ) ( ) .co ( ) ( ) . ( ) ( ) ( 3 6 /1424 Prove that( See Exercise 2Oulas Fil in the4 .4.13 . Find a basisfor the orthogonal complement of the following subspaces of R ?4126 . Proveplane 3 2 + 4y – 52 – 0 ; ( b ) the line in the direction (2 1 3 ) ; ( C ) the image of thePART Let WC2 0 2 1( d ) the cokernel of the same matrixmenformas an ortheV . then it’s art4 . 4 . 14 . Find a basis for the orthogonal complenplement of the following subspaces of R 4 : ( al thand = Cont 1set of solutions to – * + 34 – 2 2 + w( b ) the subspace spanned by ( 1 2 , – 1.31coimage of the same matrixIF , ( – 1 2 0 1 ) ; ( C ) the kernel of the matrix in Exercise 4 . 4 130 ; ( d ) the14.28 . Considerusual It inne4 . 4 . 15 . Decompose each of the following vectors with respect to the indicated subspace as( 6 ) Prove thedimensionalw + 2 , where WEW Z EW ( a ) v( 2 ) . W = span ( ( 3 )( b )( 3 ) . W = span ( ( ) . ( ) : ( ) v = ( ) . W = Ker ( 2 8Orthogonali( 2 ) v = ( 6 ) W = ing ( 2 – 1 6 ) ; ( 6 ) v = ( ) . W = Ker1 0 01 Chapter 2matrix A Ac4 .4 . 16 . Redo Exercise 4 .4 12 using the weighted inner product ( V W ) = 1 20 + 24 2 42 + 3139 ) The second tospace ) and theinstead of the dot product4 . 4 . 17 . Redo Example 4 43 with the dot product replaced by the weighted inner product(8 9 also of( V , W ) = 0 1 20 1 + 2 0 2 2 2 + 3 0 3 2 3 + 4 04 2 4subspaces are$ 4 .4 . 18 . Prove that the orthogothozonal complement Wit of a subspace WV CV is itseTheorem 4B itself a subspacecomplementsNeuronalIn general , a subset W CV of a normed vector space is dense if for every V E V , and even6 3 0 . one can find WE W with ly – will Ce. The Weierstrate Approximation TheoremTheorem 10 . 2 21 , tell us that the polynomials form a dense stopat the space of continentem , 1 19functions , and underlies the proof of the result mentioned in the preceding paragraphProof : A vematrix mal

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Is there a contradiction between our demand that our children be honest and moral persons and our demand that they be successful? Present the argument that there is a contradiction, and see if you can answer it.

Is there a contradiction between our demand that our children be honest and moral personsand our demand that they be successful? Present the argument that there is a contradiction,and see if you…

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