Redesign topsort so it selects the LAST NODE in each iteration, rather than the first.

def topsort(G):

count = dict((u, 0) for u in G) # The in-degree for each node

for u in G:

for v in G[u]:

count[v] += 1 # Count every in-edge

Q = [u for u in G if count[u] == 0] # Valid initial nodes

S = [] # The result

while Q: # While we have start nodes...

u = Q.pop() # Pick one

S.append(u)    # Use it as first of the rest

for v in G[u]:

count[v] -= 1 # "Uncount" its out-edges

if count[v] == 0: # New valid start nodes?

Q.append(v) # Deal with them next

return S

Question 1
(a) What is the objective of sampling? [2]
(b) What is the difference between a poll and a survey? [4]

(c) What is the difference between probability sampling and non-probability sampling? Give exam-
ples of both. [8]

(d) What are the sources of errors in surveys? Explain in detail giving examples. How can the
errors be reduced? [12]
(e) List all possible simple random samples of size n = 2 that can be selected from the population
{0, 1, 2, 3, 4}, and calculate s^2

for the any two samples and show that s^2=(N/N−1)σ^2




. Also calculate

σ^2 for the population and V ar( ̄y) for the two samples.

Type into Google: "globalfoundries sand to silicon", and a Youtube video will come up (accessed on 3/17/2020). The address is:

youtube.com/watch?v=UvluuAIiA50

Watch more than once if needed.

The video will go over various parts of the process steps in making a silicon computer chip integrated circuit (IC). On this page (and on the back if needed):

1. List (in order) the major steps in the fabrication process described in the video set. I do not expect you to have a detailed description of each step – just write down the "highlights".

2. Explain why the ICs are fabricated in the "clean rooms" depicted in the video.

3. A representation of the silicon crystal is used in some of the animations in the video. Explain what is wrong with the representation.

A 36 V battery of negligible internal resistance is connected to a 47 kΩ and a 21 kΩ resistor in series.

a).

What reading will a voltmeter, of internal resistance 95 kΩ , give when used to measure the voltage across the first resistor?

Express your answer using two significant figures.

V47 kΩ=

b).

What is the percent inaccuracy due to meter resistance for each case?

Express your answer using two significant figures.

V not ideal−V ideal/V ideal=

c).

What reading will a voltmeter, of internal resistance 95 kΩ , give when used to measure the voltage across the second resistor?

Express your answer using two significant figures.

V21 kΩ=

d).

What is the percent inaccuracy due to meter resistance for each case?

Express your answer using two significant figures.

V not ideal−V ideal/V ideal=

Turing machine A that does the following:

• On its first and second tape, A receives two strings w and v, w, v ∈ {0, 1}? , representing two integer numbers. When machine A is started, the tape heads are located on the left-most position, on the most significant bits of w and v.

• If none of the inputs w and v is the empty word, the Turing machine A writes the binary representation of the sum of the two integer numbers w and v on the third tape and then accepts the input. If one of w or v is the empty word, the Turing machine does not write anything on the third tape and rejects the input. If machine A outputs something, it outputs the binary representation of the sum in such a way that the left-most bit contains the most significant bit of the sum. Be careful: w and v may be of different length.

Q: Define a 3-tape Turing machine M that implements multiplication, in a manner similar to how A implements addition

3. Sketch a T-v diagram and find the specified state for the following states

a. Propane at critical temp & press find T(°C), p(bar) and v(m3 /kg)

b. Water v=.05 m3 /kg, T=140°C find p(bar)

c. Water at p=30 MPa, T=100°C find v(m3 /kg)

Suppose that over a certain region of space the electrical potential V is given by the following equation.

V(x, y, z) = 4x² − 4xy + xyz

(a) Find the rate of change of the potential at P(3, 6, 6) in the direction of the vector v = i + j − k.
???
(b) In which direction does V change most rapidly at P?

???
(c) What is the maximum rate of change at P?

???

A 40-turn coil has a diameter of 11 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.40 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil (in V) if the magnetic field is reduced to zero uniformly in the following times.

(a)

0.30 s

V

(b)

3.0 s

V

(c)

65 s

V