Figure $2\mathrm{.}8$ shows a frame $\{B\},$ which is rotated relative to frame $\{A\}$ about hat$(Z)$ by $30$

degrees, translated $10$ units in hat$(x{)}_A,$ and translated $5$ units in hat$(Y{)}_A.$ Find ${?}^{A}P,$ where

${?}^{B}P=[3\mathrm{.}07\mathrm{.}00\mathrm{.}0{]}^T$

FIGURE $2\mathrm{.}8$: Frame $(B)$ rotated and translated.