3-D rotation. Let x and y be 3-vectors representing positions in 3-D. Suppose that the vector y is obtained by rotating the vector x about the vertical axis (i.e., e3) by 45◦ (counterclockwise, i.e., from e1 toward e2). Find the 3 × 3 matrix A for which y = Ax. Hint. Determine the three columns of A by finding the result of the transformation on the unit vectors e1, e2, e3.

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