10. On a separate sheet of paper, transform the vector shown rotating it using $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$. What is the $y$-value of the terminal point of the resulting vector? \[ y= \]

Step 1 ：The problem is asking for the y-value of the terminal point of a vector after it has been transformed by a given matrix. The matrix given is a 2x2 matrix, which suggests that the vector we are transforming is a 2-dimensional vector.

Step 2 ：The transformation of a vector by a matrix is done by matrix multiplication. In this case, we are multiplying the given matrix by the vector to get the transformed vector.

Step 3 ：The y-value of the terminal point of the resulting vector is simply the second component of the resulting vector.

Step 4 ：Given that the x and y values of the vector are both 1, and the given matrix is \(\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), the transformed vector is also \([1, 1]\).

Step 5 ：Therefore, the y-value of the terminal point of the resulting vector is 1.