Let $A = \left[ \begin{array} { l l } a _ { 1 } & a _ { 2 } \\ a _ { 3 } & a _ { 4 } \end{array} \right]$ and $B = \left[ \begin{array} { l l } b _ { 1 } & b _ { 2 } \\ b _ { 3 } & b _ { 4 } \end{array} \right]$ both be rotation matrices on the coordinate plane with center at the origin $O$, rotating counterclockwise by an acute angle, and satisfying $A ^ { 2 } = B ^ { 3 } = \left[ \begin{array} { l l } 0 & c \\ 1 & d \end{array} \right]$, where $c$ and $d$ are real numbers. Let point $P ( 1,1 )$ be transformed by $A ^ { 3 }$ to point $Q$, and point $Q$ be transformed by $B ^ { 4 }$ to point $R$. Find the coordinates of point $Q$ and the angle between $\overrightarrow { O R }$ and the vector $(1, 0)$. (Non-multiple choice question, 6 points)
Let $A = \left[ \begin{array} { l l } a _ { 1 } & a _ { 2 } \\ a _ { 3 } & a _ { 4 } \end{array} \right]$ and $B = \left[ \begin{array} { l l } b _ { 1 } & b _ { 2 } \\ b _ { 3 } & b _ { 4 } \end{array} \right]$ both be rotation matrices on the coordinate plane with center at the origin $O$, rotating counterclockwise by an acute angle, and satisfying $A ^ { 2 } = B ^ { 3 } = \left[ \begin{array} { l l } 0 & c \\ 1 & d \end{array} \right]$, where $c$ and $d$ are real numbers.
Let point $P ( 1,1 )$ be transformed by $A ^ { 3 }$ to point $Q$, and point $Q$ be transformed by $B ^ { 4 }$ to point $R$.
Find the coordinates of point $Q$ and the angle between $\overrightarrow { O R }$ and the vector $(1, 0)$. (Non-multiple choice question, 6 points)