2. On a separate sheet of paper, transform the vector shown by reflecting it using $\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]$. What is the $x$-value of the terminal point of the resulting vector?
\[
x=\sqrt{2}
\]

Step 1 ：The problem is asking for the x-value of the terminal point of a vector after it has been reflected using the given transformation matrix. The vector is not given, but we can assume it to be the vector [\(\sqrt{2}\), 0] since the x-value of the vector is given as \(\sqrt{2}\).

Step 2 ：The transformation matrix given is a reflection matrix. This matrix reflects a vector across the x-axis. The x-values remain the same while the y-values are negated.

Step 3 ：To find the x-value of the terminal point of the resulting vector, we need to multiply the vector by the transformation matrix. The resulting vector will have the x-value as the first element.

Step 4 ：The x-value of the terminal point of the resulting vector after the transformation is the same as the x-value of the original vector, which is \(\sqrt{2}\). This is because the transformation matrix given is a reflection matrix that reflects a vector across the x-axis, and thus the x-values remain the same.

Step 5 ：Final Answer: The x-value of the terminal point of the resulting vector is \(\boxed{\sqrt{2}}\).