The linear transformation T: R2 R? with matrix cos 0 - sin 0 A = cos 0 rotates vectors in the ry-plane sin 0 counterclockwise through an angle 0, where 0 <0 < 2n. By arguing geometrically, determine all values of 0 for which A has real eigenvalues. Find the real eigenvalues and the corresponding eigenvectors.

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