Determine a linear transformation function that would rotate the pink figure by 105^{circ} clockwise and would dilate it by a factor of 0.75 . The general form of the linear transformation should be L(x, y)=(a x+b y, c x+d y). You must round all coefficients to four decimal places. The resulting figure should be the green shape.

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Step:1 ：Convert 105 degrees to radians: (theta_{rad} = 1.8326)Step:2 ：Find the rotation matrix: (begin{bmatrix} -0.2588 & 0.9659  -0.9659 & -0.2588 end{bmatrix})Step:3 ：Apply the dilation factor of 0.75: (begin{bmatrix} -0.1941 & 0.7244  -0.7244 & -0.1941 end{bmatrix})Step:4 ：boxed{L(x, y) = (-0.1941x + 0.7244y, -0.7244x - 0.1941y)}

Answer

Step: 1 ：Convert 105 degrees to radians: (theta_{rad} = 1.8326)Step: 2 ：Find the rotation matrix: (begin{bmatrix} -0.2588 & 0.9659  -0.9659 & -0.2588 end{bmatrix})Step: 3 ：Apply the dilation factor of 0.75: (begin{bmatrix} -0.1941 & 0.7244  -0.7244 & -0.1941 end{bmatrix})Step: 4 ：boxed{L(x, y) = (-0.1941x + 0.7244y, -0.7244x - 0.1941y)}

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