Find the 3 × 3 Matrix That Produces the Described $\left[ \begin{array} { c c c } 0.3 & - 0.4 \sqrt { 2 } & 0 \\ 0.3 \sqrt { 2 } & 0.4 & 0 \\ 0 & 0 & 1 \end{array} \right]$

Multiple Choice

Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates.
-Rotate points through 45° and then scale the x-coordinate by 0.6 and the y-coordinate by 0.8.

A)
$\left[ \begin{array} { c c c } 0.3 & - 0.4 \sqrt { 2 } & 0 \\ 0.3 \sqrt { 2 } & 0.4 & 0 \\ 0 & 0 & 1 \end{array} \right]$

B)

$\left[ \begin{array} { c c c } 0.3 \sqrt { 2 } & 0.3 \sqrt { 2 } & 0 \\ - 0.4 \sqrt { 2 } & 0.4 \sqrt { 2 } & 0 \\ 0 & 0 & 1 \end{array} \right]$

C)
$$\left[ \begin{array} { c c c } 0.3 \sqrt { 2 } & - 0.3 \sqrt { 2 } & 0 \\0.4 \sqrt { 2 } & 0.4 \sqrt { 2 } & 0 \\0 & 0 & 1\end{array} \right]$$
D)
$$\left[ \begin{array} { c c c } 0 & - 0.6 & 0 \\0.8 & 0 & 0 \\0 & 0 & 1\end{array} \right]$$