$2\mathrm{.}43$ At a given instant, a spacecraft has the position and velocity vectors $r_0=7000i(km)$ and $v_0=7$hat$(i)+7$hat$(j)(k\frac{m}{s})$ relative to an earth$-$centered nonrotating frame.

$($a$)$ What is the position vector after the true anomaly increases by $90?$

$($b$)$ What is the true anomaly of the initial point?