A satellite orbits 350 km above the Earth…

Step 1. Speed. $v = \sqrt{\dfrac{9.8\ \text{m/s}^2 \times (6.4 \times 10^{6}\ \text{m})^2}{6.75 \times 10^{6}\ \text{m}}} = 7.71\ \text{km/s}$.

Step 2. Period. $T = \dfrac{2\pi \times 6.75 \times 10^{6}\ \text{m}}{7710\ \text{m/s}} = 5500\ \text{s} = 91.7\ \text{min}$.