Determine the Laplace transforms of (a) \( 2 t \), (b) \( \sin 2 t \), (c) a unit impulse at time \( t=2 \mathrm{~s} \), (d) \( 4 \mathrm{~d} x / \mathrm{d} t \) when \( x=2 \) at \( t=0 \), (e) \( 3 \mathrm{~d}^{2} x / \mathrm{d} t^{2} \) when \( x=0 \) and \( \mathrm{d} x / \mathrm{d} t=0 \mathrm{at} t=0 \), (f) the integral between \( t \) and 0 of \( \mathrm{e}^{-t} \).