The notion of orthogonal map

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Let $L:\mathbb{R}^2\to \mathbb{R}^2$ be an orthogonal map with determinant $1$ satisfying

$L(\rv{1,0} ) =\dfrac{1}{17}\,\rv{15,-8}$ Determine the image under $L$ of the second standard basis vector.

$L(\rv{0,1} ) =$

$\rv{\Box,\Box}$

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