Ononot — A transformation T: \mathbb{R}^2 \to \mathbb{R}^2 is given b

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Transformationshard

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A transformation $T: \mathbb{R}^2 \to \mathbb{R}^2$ is given by $T(\mathbf{x}) = M\mathbf{x} + \mathbf{b}$ where $M = \begin{pmatrix} \cos \theta & \sin \theta \\ \sin \theta & -\cos \theta \end{pmatrix}$ . Which of the following statements about $T$ is correct?