1. The volume of a cylinder is pi*r^2*h. Define r as 3 and h as the matrix h = [1,5,12] find the volume of the cylinders. 2. The area of a triangle is (1/2)"base"height. Define the base as the matrix b = [2,4,6] and the height h as 12, and find the area of the triangles. 3. The volume of any right prism is (base_area)*(vertical_dimension). Find the volumes of the prisms with triangles of Problem 2 as their bases, for a vertical dimension of 10. 4. Generate an evenly spaced vector of values from 1 to 20, in increments of 1. (Use the linespace command). 5. Generate a vector of values from zero to 2*pi in increments of pi/100. (Use the linespace command). 6. Generate a vector of containing 15 values, evenly spaced between 4 and 20. (Use the linespace command). 7. The general equation for the distance that a free falling body has traveled (neglecting air friction) is d = (1/2)*g*t^2. Assume that g = 9.8 m/s^2. Generate a table of time distance traveled, for time from 0 to 100 s in increments of 10 s. Be sure to use element-by-element operations, not matrix operations. 8. Newton's law of universal gravitation tells us that the force exerted by one particle on another is F G (m_1*m_2)/(r^2) where the universal gravitational constant is found experimentally to be G = 6.673*10^-11 N m^2/kg^2 The mass of each object is m_1 and m 2, respectively, and r is the distance between the two particles. Use Newton's law of universal gravitation to find the force exerted by the earth on the moon, assuming that: the mass of the earth is approximately 6*10^24 kg,the mass of the moon is approximately 7.4*10^22 kg, and the earth and the moon are an average of 3.9*10^8 m apart.