Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j

Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).

The distance S metres moved by a body in t seconds is given by \(S = 5t^3 - \frac{19}{2} t^2 + 6t - 4\). Calculate the acceleration of the body after 2 seconds

Evaluate \(\int^1_0 x(x^2-2)^2 dx\)

Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).