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\newcommand{\ds}{\displaystyle}
\newcommand{\pl}{\partial}
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\begin{document}


{\bf Question}

Find the matrix which describes the following transformation:
\begin{description}
\item[(i)] a rotation about the origin through $\frac{\pi}{3},$
\item[(ii)] a reflection in the y-axis,
\item[(iii)] a reflection in the straight line passing through
the origin and (1,1).
\end{description}

\vspace{.25in}

{\bf Answer}

\begin{description}
\item[(i)] $\left( \begin{array}{cc} \ds \frac{1}{2} & \ds
-\frac{\sqrt 3}{2} \\ \ds \frac{\sqrt 3}{2} & \ds \frac{1}{2}
\end{array} \right)$

${}$

\item[(ii)] $ \left( \begin{array}{cc} -1 & 0 \\ 0 & 1 \end{array}
\right)$

${}$

\item[(iii)] $\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}
\right)$
\end{description}

\end{document}
