A rotation centered at the origin takes $\begin{pmatrix} 13 \\ 0 \end{pmatrix}$ to $\begin{pmatrix} 5 \\ -12 \end{pmatrix}.$  Which vector does the rotation take $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ to?
Question:
A rotation centered at the origin takes $\begin{pmatrix} 13 \\ 0 \end{pmatrix}$ to $\begin{pmatrix} 5 \\ -12 \end{pmatrix}.$  Which vector does the rotation take $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ to?
Answer:
Let's think step by step.

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\begin{pmatrix} 12/13 \\ 5/13 \end{pmatrix}
A rotation centered at the origin takes $\begin{pmatrix} 13 \\ 0 \end{pmatrix}$ to $\begin{pmatrix} 5 \\ -12 \end{pmatrix}.$  Which vector does the rotation take $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ to?
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