The volume of a cylinder is V space equals space pi space r squared space h, where r is the radius of the circular faces and h is the height of the cylinder. Your measurements show that the mean value of r is 21 cm and its statistical and instrumental uncertainties turned out to be 0.10 cm and 0.20 cm, respectively. Likewise, that of h are 13 cm for the mean, 0.2 cm (statistical) and 0.3 cm (instrumental) for its uncertainties. What can you say about which source of uncertainty has the largest contribution to the overall uncertainty of V ? What would you need to do to improve (reduce) the uncertainty on your calculation of V?

Explain each of the following (in your own words):

a. The 3 fundamental rules of subprograms

b. Subprogram

c. Subprogram call

d. Subprogram Header

e. Parameter profile/Protocol

f. Formal Parameter–v-Actual Parameter

g. Procedure –v-Function

h. Design issues for subprograms

i. Stack dynamic –v-static variables

j. Parameter passing

i. In-mode

ii. Out-mode

iii. In-Out mode

1.Pass by result

2.Pass by reference

3.Pass by name

k. Design issues for parameter passing

l. Overloaded subprogram

m. Generic subprogram

n. Design issues for functions

A satellite of mass m is launched from the Earth’s surface at v that is slightly less than the escape speed vesc. The ratio of the satellite launch speed v to the escape speed vesc is defined as f = v/vesc. The satellite is launched straight up. Before coming back down, the satellite momentarily comes to a stop at an altitude h above the surface of the Earth. (a) In terms of the satellite launch speed ratio f, Re, and other needed parameters, what is the maximum height h (6 points)? (b) Let f = v/vesc = 0.92136. What is the altitude h for this f? The mass and radius of the Earth (Me and Re) are 5.97 x 1024 kg and 6,371 km respectively (3 points).Assume this satellite goes into a circular orbit around the Earth at the altitude h calculated in 8(b) above. What is the period (T) in days for this orbit (6 points)? (d) What is special about the orbit with the period calculated in 8(c) above? Carefully explain your answer (2 points)

Using the mass of KCl, calculate the actual concnetration of k+ in the stock solution (approximately 1000 ppm w/v)??

Mass used = 0.4773g KCl

Dissolved 0.4773g KCl in a 250ml Volumetric flask.

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Calculate the actualy concentration of K+ in the diluted stock solution??

***I took 25ml of the stock solution and put it in another 250ml volumetric flask, then filled to volume with water in order to prepare 250.00ml of approxmately 100ppm w/v k+.

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Calculate the actualy concnetrations (in ppm w/v) of K+ in your calibration standard solutions??

***I took 5 100ml volumetric flask to prepare solutions that are approximately 1, 2, 3, 4, and 5 ppm w/v k+.

-To do that, i took 1 ml of the dilute stock solution and place in one of the 100ml voumetric flask. Then filled to volume with water

-I took 2ml of the dilute stock solution and placed in another 100ml volumetri flask, then filled to volume with water

-I did the same thing with the 3, 4, and 5.

1. A magnet is inserted into a coil of wire consisting of 10000 loops. The cross-sectional area of the coil is 0.5 m²and is kept in a uniform magnetic field of B = 4 T. Assume that the angle between the surface normal of the coil and magnetic field is q_o= 45^oat t₀= 0s. The coil is rotated at a constant rate to an angle, q= 90⁰at t = 60s. What is the average induced voltage (emf) induced in the coil?

A) 177 V        B) 220 V         C) 288.70 V    D) 235.70 V

2. To have stationary interference pattern in young double slit experiment, wavelength of incident beams should be:

A) Same         B) different      C) zero D) Infinite

3. If we switch from red laser (l= 670nm) to green laser (l= 530nm) in a Young’s double slit diffraction experiment then what happens to the fringe pattern?

A) Nothing     B) Position of the Principle maxima changed by 130 nm.

C) Separation between fringes increases.       D) Separation between fringes decreases

You have recently commenced work for the Australian taxation division of YE International LLP an international accounting partnership. A partner in the Houston Texas office has contacted you and stated that one of his clients has a partly owned subsidiary in Australia that has asked him questions about four Australian Tax law cases, and accordingly he has told them that he would obtain an analysis of the cases. He is accordingly requesting you to provide the analysis for him to pass to the client. The cases are: 1st Tax Case: SNF (Australia) Pty Ltd v FC of T (2011) 193 FCR 149 2nd Tax Case: Resource Capital Fund IV LP v Commissioner of Taxation [2019] FCAFC 51 3rd Tax Case: Burton v Commissioner of Taxation [2019] FCAFC 141. 4thTax Case: Chevron Australia Holdings Pty Ltd (CAHPL) v Commissioner of Taxation [2017] FCAFC 62

Question 1. Let V and W be finite dimensional vector spaces over a field F with dimF(V ) = dimF(W) and let T : V → W be a linear map. Prove there exists an ordered basis A for V and an ordered basis B for W such that [T] A B is a diagonal matrix where every entry along the diagonal is either a 0 or a 1.

Hint 1. Suppose A = {~v1, . . . , ~vn} and B = { ~w1, . . . , ~wn}. If the k th column of [T] A B consists of all zeros, what can you deduce?

Hint 2. Suppose A = {~v1, . . . , ~vn} and B = { ~w1, . . . , ~wn}. If the k th column of [T] A B has a one in the k th entry and all other entries are zero, what can you deduce?

Hint 3. Now construct bases with the properties found in Hint 1 and Hint 2.

Hint 4. Theorem 18 part 5 is your friend.

Hint 5. The proof of the Rank-Nullity Theorem is your best friend.

A project requires an initial investment of $1,000,000 and is depreciated straight-line to zero salvage over its 10-year life.

The project produces items that sell for $1,000 each, with variable costs of $700 per unit. Fixed costs are $350,000 per year.

 What is the accounting break-even quantity? o Q = (FC + D)/(P – v)

 What is the operating cash flow at accounting break-even? o OCF= [PQ - vQ – FC – D] + D

•  What is the cash break-even?
  o Q = (FC + OCF)/(P – v); where OCF=0

•  What is the financial break-even? I = 10%

o Find OCF where NPV = 0, Q = (OCF + FC) / (P – v)

Show all work as follows:

Identify:

•  FC = Fixed Cost

•  D = Depreciation

•  P = Price

•  v = variable cost per unit

•  OCF = operating cash flow (if needed)

  Then compute the break-even quantities.

Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much larger than the field around the body of the airplane and can become large enough to produce dielectric breakdown of the air, discharging the airplane. To model this process, assume that two charged spherical conductors are connected by a long conducting wire and a charge of 79.0 µC is placed on the combination. One sphere, representing the body of the airplane, has a radius of 6.00 m, and the other, representing the tip of the needle, has a radius of 2.00 cm.

(a) What is the electric potential of each sphere? r = 6.00 m: ]V

r = 2.00 cm: V

(b) What is the electric field at the surface of each sphere?

r = 6.00 m: magnitude____________ V/m? direction_________?

r = 2.00 cm: magnitude ____________ V/m? direction________?