Question

(each [] is a new row in the matrix)
Find the coordinates of the image of: [0, 1,-3][0, 8, 9] after a rotation of 270 degrees.

Accepted Answer

The matrix of rotation is the following:

R = \left( \begin{array}{cc} \cos \alpha & \sin \alpha \\ - \sin \alpha & \cos \alpha \end{array} \right) = \left( \begin{array}{cc} \cos 270{}^\circ & \sin 270{}^\circ \\ - \sin 270{}^\circ & \cos 270{}^\circ \end{array} \right) = \left( \begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array} \right).

The image is:

RA = \left( \begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array} \right) * \left( \begin{array}{ccc} 0 & 1 & -4 \\ 0 & 8 & 9 \end{array} \right) = \left( \begin{array}{ccc} 0 & -8 & -9 \\ 0 & 1 & -4 \end{array} \right).

Question #6320

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