11. As shown in the figure, a rectangular prism $ABCD - EFGH$ has edge length equal to 2 (i.e., $\overline{AB} = 2$). $K$ is the center of square $ABCD$, and $M$, $N$ are the midpoints of segments $BF$ and $EF$ respectively. Which of the following options are correct?\\
(1) $\overrightarrow{KM} = \frac{1}{2}\overrightarrow{AB} - \frac{1}{2}\overrightarrow{AD} + \frac{1}{2}\overrightarrow{AE}$\\
(2) (Dot product) $\overrightarrow{KM} \cdot \overrightarrow{AB} = 1$\\
(3) $\overline{KM} = 3$\\
(4) $\triangle KMN$ is a right triangle\\
(5) The area of $\triangle KMN$ is $\frac{\sqrt{10}}{2}$\\
\includegraphics[max width=\textwidth, alt={}, center]{0ae6c49a-bce7-460f-aba8-c0069d0851f1-5_492_492_461_1064}

\section*{Part II: Fill-in-the-Blank Questions (45 points)}
Instructions: 1. For questions A through I, mark your answers on the ``Answer Sheet'' at the row numbers indicated (12–33). 2. Each completely correct answer is worth 5 points; incorrect answers do not result in deductions; incomplete answers receive no credit.

A. From the positive integers 1 to 100, after removing all prime numbers, multiples of 2, and multiples of 3, the largest remaining number is (12)(13).

B. On the coordinate plane, there are four points $O(0,0)$, $A(-3,-5)$, $B(6,0)$, $C(x,y)$. A particle starts at point $O$ and moves in the direction of $\overrightarrow{AO}$ for a distance of $\overline{AO}$ and stops at $P$. Then it moves in the direction of $\overrightarrow{BP}$ for a distance of $2\overline{BP}$ and stops at $Q$. Suppose the particle continues to move in the direction of $\overrightarrow{CQ}$ for a distance of $3\overline{CQ}$ and returns to the origin $O$. Then $(x, y) = ($（14）（15），（16）（17）$)$.

C. In a raffle game, participants draw a ball from a box, confirm its color, and return it. Only those who draw a blue or red ball receive a shopping voucher with amounts of 2000 yuan (for blue ball) and 1000 yuan (for red ball) respectively. The box currently contains 2 blue