Solution to 2001 Problem 75

If you apply the matrix to the vector (1,0,0) you get (1/2, -\sqrt{3}/2,0) which means that the matrix rotates vectors 60 ^{\circ} clockwise about the z axis. We are told that both (a_x', a_y', a_x') and (a_x, a_y, a_z) represent the same vector. Therefore, the reference frame S must be rotated 60 ^{\circ} counterclockwise about the z axis so that (1/2, -\sqrt{3}/2,0) represents the same vector as (1,0,0) in the initial reference frame. Therefore, answer (E) is correct.

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