'Let T R2 4 R2 denote the linear transformation which rotates the plane counterclockwise through an angle of 45 degrees Write out anl explicit formula for T. Use it to compute T'
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Assume that T is a linear transformation. Find the standard matrix of T. (a) T: R^2 → R^2 first reflects points through the vertical x_2-axis and then reflects points through the line x_2 = x_1. (b) T: R^2 → R^2 first rotates a point (about the origin) through π/4 radians (counterclockwise) and then reflects points through the horizontal x_1-axis.
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In Exercises $1-10$ , assume that $T$ is a linear transformation. Find the standard matrix of $T$ . $T : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ first rotates points through $-3 \pi / 4$ radian (clockwise) and then reflects points through the horizontal $x_{1}$ -axis. $\left[\text { Hint } : T\left(\mathbf{e}_{1}\right)=(-1 / \sqrt{2}, 1 / \sqrt{2}) .\right]$
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