105PS2 - by the transformation T Is the combined...

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UNIVERSITY OF CALIFORNIA AT BERKELEY DEPARTMENT OF PHYSICS PHYSICS 105 SPRING SEMESTER 2009 LEROY T. KERTH Problem Set 2 Due February 9, 2009 1. Find the values of å needed to make the following transformation orthogonal. 1 0 0 0 ! " 0 # $ % % % ( ( ( 2. In class we found a rotation about the z-axis buy the angle is given by the matrix: RotZ = cos sin 0 " sin cos 0 0 0 1 # $ % % % ( ( ( Consider another orthogonal transformation: T = ! 1 0 0 0 1 0 0 0 1 " # $ $ $ % Write the matrix for a rotation about the z-axis followed
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Unformatted text preview: by the transformation T. Is the combined transformation orthogonal? Is it a proper rotation? Describe the effect of the transformation T in words and a sketch. Now consider the transformation ! T following RotZ : ! T = " 1 " 1 1 # $ % % % & ’ ( ( ( 3. 1.37 page 39 4. 1.46 page 40 5. 2.16 page 75 6. 2.21 page 75 7. 3.3 page 99...
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