Find the Standard Matrix of the Linear Transformation T $\mathfrak { R } ^ { 2 } \rightarrow > \mathfrak { R } ^ { 2 }$

question 24

Multiple Choice

Find the standard matrix of the linear transformation T.
-T: $\mathfrak { R } ^ { 2 } \rightarrow > \mathfrak { R } ^ { 2 }$ rotates points (about the origin) through $\frac { 7 } { 4 } \pi$ radians (with counterclockwise rotation for a positive angle) .

• A) \(\left[\begin{array}{c} \frac{\sqrt{3}}{3} \frac{\sqrt{3}}{3} \\ -\frac{\sqrt{3}}{3} \frac{\sqrt{3}}{3} \end{array}\right]\)
• B) \(\left[\begin{array}{c} -\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \\ -\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \end{array}\right]\)
• D) \(\left[ \begin{array} { r r } 1 & 1 \\ - 1 & 1 \end{array} \right]\)

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