Find the standard matrix representation for each linear operator L : R^2 → R^2 described below: (a) L rotates each vector x by 45◦ in the clockwise direction. (b) L reflects each vector x about the x1 axis and then rotates it 90◦ in the counterclockwise direction. (c) L doubles the length of x and then rotates it 30◦ in the counterclockwise direction. (d) L reflects each vector x about the line x2 = x1 and projects it onto the x1 axis.

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