5 A uniform lamina has the shape of the region enclosed by the curve \(y = x ^ { 2 } + 1\) and the lines \(x = 0 , x = 4\) and \(y = 0\) The diagram below shows the lamina.
\includegraphics[max width=\textwidth, alt={}, center]{4975a2a9-1e45-44b4-b525-fc902627d03e-06_613_447_500_794} 5

1. Find the coordinates of the centre of mass of the lamina, giving your answer in exact form.
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2. The lamina is suspended from the point where the curve intersects the line \(x = 4\) and hangs in equilibrium. Find the angle between the vertical and the longest straight edge of the lamina, giving your answer correct to the nearest degree.
   \includegraphics[max width=\textwidth, alt={}, center]{4975a2a9-1e45-44b4-b525-fc902627d03e-08_2488_1730_219_141}