3. Consider the previously defined coordinate systems $F_{EC}$ and $F_E$. Denote latitude by
the symbol $\lambda$ and longitude by the symbol $\mu$. Measure latitude positive north and
negative south of the equator, $-90 \text{ deg} \le \lambda \le +90 \text{ deg}$. Measure longitude positive
east and negative west of zero longitude, $-180 \text{ deg} < \mu \le +180 \text{ deg}$.
(a) Given the latitude $\lambda_E$ and longitude $\mu_E$ of $F_E$, find a transformation matrix from
$F_{EC}$ to $F_E$ ($T_{E,EC}$) that is a function only of $\lambda_E$ and $\mu_E$.
(b) Using your answer to part 3a, transform the Earth's rotation vector in $F_{EC}$
to its representation in Earth-fixed coordinates at Blacksburg, Virginia, USA
($F_E = F_{BBurg}$). That is, transform {$\omega_E$}$_{EC}$ to {$\omega_E$}$_{BB}$. Use $\lambda_{BBurg} = 37^\circ 12.442''N$,
$\mu_{BBurg} = 80^\circ 24.446''W$.
4 Consider the Euler angles involved in 201
