Q3. A)

I. Put the following sentences into their Clausal Elements:

Eg. John / danced / yesterday. S V A

i. Seeing is believing.

ii. I wish you good luck.

iii. What he said at the meeting was completely balderdash.

iv. Out of joy, the lecturer appointed Collins the course representative immediately.

v. Gyesi scores the third goal for Oasis FC in every competition.

II. Construct a Meaningful Sentence for EACH of the Following Patterns

i. SAVC

ii. ASVOC

iii. SVOA

iv. SVOCA

v. AASVC

Let A ∈ Mat n×n(R) be a real square matrix.

(a) Suppose that A is symmetric, positive semi-definite, and orthogonal. Prove that A is the identity matrix.

(b) Suppose that A satisfies A = −A^T . Prove that if λ ∈ C is an eigenvalue of A, then λ¯ = −λ.

From now on, we assume that A is idempotent, i.e. A^2 = A.

(c) Prove that if λ is an eigenvalue of A, then λ is equal to 0 or 1.

(d) Set V1 = {v ∈ C n | Av = v} and V0 = {v ∈ C n | Av = 0}. Show that im A = V1 and ker A = V0.

(e) Prove that A is diagonalizable.

You are testing a new GPS system for general aviation aircraft and have encountered some unexplained heating. Modeling the circuit as three resistors in series, R₁ (2 Ω) is known while R₂ and R₃ are not. We measure voltage drops of V₁= 1 V, V₂ = 50 V, and V₃ = 100 V respectively across the three resistors. Determine the resistance of the unknown resistors.

In addition to the above calculations, explain to a member of upper management why anomalous heating in this circuit is related to determining these values and hence may be beneficial to the future design operations.  

The grammar below generates a tiny subset of English sentences, without worrying much about subject-verb agreement:

G = {

S → NP VP

NP → the Adj N | N

VP → V | V NP

Adj → happy | angry | ε |

V → chases | growls | purrs

N → cat | dog

}

Convert G into Chomsky Normal Form. When eliminating rules that mix terminals and non-terminals on the RHS of a rewrite rule, add needed rules only, and please use the form X_word → word (e.g., X_the → the).

Type or paste question here

Suppose that a parallel-plate capacitor has circular plates with radius R = 60.0 mm and a plate separation of 4.6 mm. Suppose also that a sinusoidal potential difference with a maximum value of 360 V and a frequency of 120 Hz is applied across the plates; that is

V=(360.0 V)sin((2.*π)*(120 Hz * t)).

Find Bmax(R), the maximum value of the induced magnetic field that occurs at r = R.

Find B(r = 30.0 mm).

Find B(r = 120.0 mm).

Find B(r = 180.0 mm).

PLEASE WRITE ANSWER IN YOUR OWN WORDS BECASUE I HAVE TO SUBMIT THE ANSWER ON TURTIN

1. Provide an appropriate answer to the following questions:

a. What are the main differences between preference shares and ordinary shares? Explain.

b. Explain the concept of “Diversification” in finance.

c. Explain the terms systematic risk and unsystematic risk.

d. Explain each of the components of the Weighted Average Cost of Capital formula below:

WACC = [ D/V × (1 − Tc)r_debt] + (E/V × r_equity)

D =

V =

Tc =

r_debt =

E=

r_equity =

For each reaction listed, determine its standard cell potential (in V) at 25°C and whether the reaction is spontaneous at standard conditions.

(a)

Co²⁺(aq) + Mg(s) → Co(s) + Mg²⁺(aq)

ΔE° = V

(b)

2 Al(s) + 3 Cu²⁺(aq) → 2 Al³⁺(aq) + 3 Cu(s)

ΔE° = V

(c)

Ag(s) + Cu(NO₃)₂(aq) → AgNO₃(aq) + CuNO₃(aq)

ΔE° =

(d)

Ni(s) + Zn(NO₃)₂(aq) → Ni(NO₃)₂(aq) + Zn(s)

ΔE° =

An object with mass 40.5 kg is given an initial downward velocity -3ms in a medium that exerts a resistive force with magnitude proportional to the square of the speed. The resistance is 80 N when the velocity is -4m/s. Use g=10m/s^2

a. Write out a differential equation in terms of the velocity v, and acceleration a



b. Find the velocity v(t) for the object

v(t)=

c. Upload a document with the work for parts a and b and a computer generated solution curve with a window appropriate for this situation.




d. State and interpret the end behavior for the solution found in part b.

Q1- V Company had the following select transactions.

Apr. 1, 2017 Accepted G Company’s 12-month, 12% note in settlement of a $30,000 account receivable.

July 1, 2017 Loaned $25,000 cash to T on a 9-month, 10% note.

Apr. 1, 2018 Received principal plus interest on the G note.

Apr. 1, 2018 T dishonored its note; V expects it will eventually collect.

Instructions Prepare journal entries to record the transactions. V prepares adjusting entries once a year on December 31.

Five kilograms of ammonia (NH3) undergo a refrigeration cycle
detailed as:
• Process 1-2: isothermic expansion from saturated vapor at 10ºC, to P = 3 bar with
Q = 400 kJ.
• Process 2-3: isochoric cooling to 0 ◦C.
• Process 3-4: isobaric compression.
• Process 4-1: isochoric heating.

Calculate:

a) the P −v and T −v diagrams.

b) the states table detailing P, v, T and u.
c) the process table for Q, W and ∆U.
d) the performance coefficient, β, of the cycle.