The rotation matrix R = cosy sinf sin0 cost 10. applied to the vector x = has the
Chapter 6, Problem 9(choose chapter or problem)
The rotation matrix R = cosy sinf sin0 cost 10. applied to the vector x = has the geometric effect o Xi *2 a. b. rotating x counterclockwise through the angle 9 radians. Let y = RftX. Verify that y is x rotated by 9. [Hint: Use the relation x\ + ixi = re'", where r = Jxf+ x? and a = tan"1 {2-). Show that y = y, + /y2 = rei(e+a).] *1 Find R^ in two different ways. [Hint: Consider a rotation in the clockwise direction.] 2 and # = | Find the rotation ofx through the angle 9 in both the counterclockwise and clockwise directions by using Re and R^1 Find the determinant of both Ri, and R
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