Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other. 
选项为:A:$$31 \frac{2}{11}$$  B:$$31 \frac{3}{11}$$  C:$$32 \frac{8}{11}$$  D:$$33 \frac{3}{11}$$  E:None of the above  请回答其中一个选项.