1. Earth is approximately a sphere of radius 6.37 x 10"m. What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers? 2. (a) Assuming that water has a density of exactly 1 g/cma, find the mass of one cubic meter of water in kilograms. (b) Suppose that it takes 10.0 h to drain a container of 5700 m of water. What is the "mass flow rate," in kilograms per second, of water from the container? 3. Water is poured into a container that has a small leak. The mass m of the water is given as a function of time : by m =5.007 -3.00f + 20.00, with / = 0, m in grams, and f in seconds. (a) At what time is the water mass greatest, and what is that greatest mass? (b) In kilograms per minute, what is the rate of mass change at r = 2.00 s and at f = 5.00 s?A vector a in the xy plane with the direction of 250" counterclockwise from the positive direction of the x axis and its magnitude is 710 m. What are (a) the x component and (b) the y component of a vector a?Consider two displacements, one of magnitude 3 m and another of magnitude 4 m. Show how the displacement vectors may be combined to get a resultant displacement of magnitude (a) 7 m, (b) 1 m, and (c) 5 m.(a) In unit-vector notation, what is the sum a + b if a =4.01 + 3.0k and b =-13.01 +7.0j? (b) What are the magnitude and direction of a + b?Three vectors are given by a = 3.01+3.0/-2.0k, b= -1.01-4.0/+2.0k, and @ =2.01+2.0j+1.0k. Find (a) a . (bx 2) (b) a . (b + q), and (c) a x (b+2)Use the difinition of schalar product a - b = ab cose and the fact that a . b= axb, + abytazbz. Calculate the angle between two vectors given by a = 3.07+3.0/ +3.0k and b =2.0/ +1.0/+3.0k