Vince works on a construction site.

The amount Vince gets paid depends on the type of shift he works, as shown in the table below.

\begin{array}{|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Shift type} \rule[-1ex]{0pt}{0pt}& \textbf{Normal} & \textbf{Overtime} & \textbf {Weekend} \\
\hline
\rule{0pt}{2.5ex} \textbf{Hourly rate of pay} \rule[-1ex]{0pt}{0pt} \ \text{(\$ per hour)} & 36 & 54 & 72 \\
\hline
\end{array}

This information is shown in matrix \(R\) below.

\begin{align*}
R=\left[\begin{array}{lll}
36 & 54 & 72
\end{array}\right] \end{align*}

1. Matrix \(R^T\) is the transpose of matrix \(R\).
2. Determine the matrix \(R^T\).   (1 mark)
   

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During one week, Vince works 28 hours at the normal rate of pay, 6 hours at the overtime rate of pay, and 8 hours at the weekend rate of pay.

2. Complete the following matrix calculation showing the total amount Vince has been paid for this week.  (1 mark)
   

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Vince will receive $90 per hour if he works a public holiday shift.

Matrix \(Q\), as calculated below, can be used to show Vince's hourly rate for each type of shift.

\begin{align*}
\begin{aligned}
Q & =n \times\left[\begin{array}{llll}
1 & 1.5 & 2 & p
\end{array}\right] \\
& =\left[\begin{array}{llll}
36 & 54 & 72 & 90
\end{array}\right] \end{aligned}
\end{align*}

3. Write the values of \(n\) and \(p\).  (1 mark)
   

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