1. \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors.]

A particle \(Q\) of mass 0.5 kg is moving on a smooth horizontal surface. Particle \(Q\) is moving with velocity \(( 3 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse of \(( 2 \mathbf { i } + 5 \mathbf { j } ) \mathrm { Ns }\).

1. Find the speed of \(Q\) immediately after receiving the impulse. As a result of receiving the impulse, the direction of motion of \(Q\) is turned through an angle \(\theta ^ { \circ }\)
2. Find the value of \(\theta\)