answer:Solution: ((1)) (overrightarrow{AB}=(-2,-1,3)), (overrightarrow{AC}=(1,-3,2)), Therefore, (overrightarrow{AB} cdot overrightarrow{AC} = -2 + 3 + 6 = 7), (|overrightarrow{AB}|= sqrt{4+1+9}= sqrt{14}), (|overrightarrow{AC}|= sqrt{1+9+4}= sqrt{14}), Therefore, (cos < overrightarrow{AB}, overrightarrow{AC} > = frac{overrightarrow{AB} cdot overrightarrow{AC}}{|overrightarrow{AB}||overrightarrow{AC}|}= frac{7}{sqrt{14} times sqrt{14}}= frac{1}{2}). ((2)) From ((1)), we know (sin ∠BAC= sqrt{1-(frac{1}{2})^2}= frac{sqrt{3}}{2}), Therefore, (S_{triangle ABC}= frac{1}{2} times |AB| times |AC| times sin ∠BAC= frac{1}{2} times sqrt{14} times sqrt{14} times frac{sqrt{3}}{2}= frac{7sqrt{3}}{2}), Therefore, the area of the parallelogram with sides (AB) and (AC) is (S=2S_{triangle ABC}=7sqrt{3}). Thus, the answers are: ((1)) (cos < overrightarrow{AB}, overrightarrow{AC} > = boxed{frac{1}{2}}) ((2)) The area of the parallelogram is (boxed{7sqrt{3}}).

answer:1. **Identify the numbers with 7 as the ones digit under 50**: The numbers are 7, 17, 27, 37, 47. 2. **Check each number for primality**: - 7 is prime. - 17 is prime. - 27 is not prime (divisible by 3). - 37 is prime. - 47 is prime. 3. **Count the prime numbers**: The prime numbers in the list are 7, 17, 37, 47. There are 4 such numbers. 4. **Conclusion**: The number of primes less than 50 that have 7 as the ones digit is 4. The final answer is boxed{C}.

answer:To find out how many people can sit in each chair, we first need to determine the total number of chairs in the church. Since there are 6 chairs in each row and there are 20 rows, we can calculate the total number of chairs by multiplying the number of chairs per row by the number of rows: Total number of chairs = Number of chairs per row × Number of rows Total number of chairs = 6 chairs/row × 20 rows Total number of chairs = 120 chairs Now, we know that the church is full when there are 600 people sitting in the chairs. To find out how many people can sit in each chair, we divide the total number of people by the total number of chairs: Number of people per chair = Total number of people / Total number of chairs Number of people per chair = 600 people / 120 chairs Number of people per chair = 5 people/chair Therefore, each chair can hold boxed{5} people.

answer:(1) **Analysis** The problem involves the division operation of complex numbers. We can solve it according to the rules of operation. **Solution** frac{2-i}{3+4i} = frac{(2-i)(3-4i)}{(3+4i)(3-4i)} = frac{2-11i}{25} = frac{2}{25} - frac{11}{25}i, Hence, the answer is boxed{frac{2}{25} - frac{11}{25}i}. (2) **Analysis** This problem involves the operation of derivatives. First, find the derivative function, then substitute x=2 to find the expression, and then solve the problem. **Solution** f'(x)=2x+3f'(2), substituting x=2 gives f'(2)=-2, hence f'(x)=2x-6, 1+f'(1)=1+2-6=-3. Hence, the answer is boxed{-3}.