Question Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as – 3i + 5j. u = (b) Oppositely directed to 12i – 6j + 24k. — V = (c) Same direction as the vector from the point A(-1,0, 2) to the point B(3,1,1). W =

Use cylindrical coordinates to calculate the triple integral lw f(x, y, z) dV for the function f(x, y, z) = 2704 2V x2 + y2 and the region x² + y2 sz s 52 – (x2 + y2). (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Ball Hits Wall 1 234567 A racquet ball with mass m 0.233 kg is moving toward the wall at v 18.5 m/s and at an angle of e 26 with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t 0.071 s.

Calculate the fermi energy of a good conductor which has number of conduction unit electrons per volume = 5.9× 10 28 /m 3 7.06 eV 5.54 eV 11.6 eV 2.21 eV Calculate the fermi energy of a good conductor which has number of conduction unit electrons per volume = 5.9× 10 28 /m 3 7.06 eV 5.54 eV 11.6 eV 2.21 eV

Consider the quadric surface given by 314 22 – 216 x y - 48 x z + 404 y2 + 72 yz +250 22 = 3025 (a) Express this equation in the form x? Ax = 3025 where A isa symmetric matrix and x = y Enter the matrix A in the box below a ab sina 8 a 12 E aac (b) You are given that the matrix A has eigenvalues 242, 242 and 484. Hence the equation of the surface in terms of its principal exes X, Y and Z can be written as 242 x 2 +242 Y2 + 484 22 = 3025 Enter the shortest distance, in Maple syntax, from the origin to the surface in the box below. Note: Use sqrt command when necessary.

2. A 2-wire d.c. distributor, 500 m long is fed at one of its ends. The cross-sectional area of each conductor is 3-4 cm and the resistivity of copper is 1-7 uNcm. The distributor supplies 200 A at a distance of 300m from the feeding point and 100 A at the terminus. Calculate the voltage at the feeding end if the voltage at the terminus is to be 230 V. [241 V]

Many companies are undergoing server virtualization. This is the concept of putting multiple “virtual” servers onto one physical device. The payoffs can be significant: fewer servers, less electricity, less generated heat, less air conditioning, less infrastructure and administration costs, increased flexibility, less physical presence (that is, smaller server rooms), faster maintenance of servers, and more. There are costs, of course, such as licensing the virtualization software, labour costs in establishing the virtual servers onto a physical device, labour costs in updating tables, and access. But determining the return on investment can be a challenge. Some companies have lost money on server virtualization, while most would say that they have gained a positive return on investment but have not really quantified the results. (a) How might a company really determine the return on investment for server virtualization? (b) Is this a project that a systems analyst might be involved in? Why or why not?