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Matrix Representations

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Multiple Choice

Which of the following matrices represents a rotation of 45 degrees about the origin in the $xy$-plane?

  1. $$\begin{bmatrix} \cos 45° & -\sin 45° \\ \sin 45° & \cos 45° \end{bmatrix}$$
  2. $$\begin{bmatrix} \cos 45° & \sin 45° \\ -\sin 45° & \cos 45° \end{bmatrix}$$
  3. $$\begin{bmatrix} \cos 45° & 0 \\ 0 & \cos 45° \end{bmatrix}$$
  4. $$\begin{bmatrix} \cos 45° & 0 \\ 0 & -\cos 45° \end{bmatrix}$$
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