B = {red,red,green,purple}
C = {red,{green},red,{red,green},purple,{green,green,red,purple}}

A.) What is the power set of C?

B.) Is B ∈ P(C)?

Draw bifurication diagram of:

(x^2-a)(x^2-4)

Again considering y'' + 4y' + 3y = 0:

(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where α > 0.

(b) Determine the coordinates (tm,ym) of the maximum point of the solution as a function of α.

(c) Determine the behavior of tm and ym as α →∞.

Consider the following system of equations for all problems.
The following system of equations is designed to determine concentrations (the c’s in g/m3) in a series of coupled reactors as a function of the amount of mass input to each reactor (the right-hand sides in g/day).

8?1 − 4?2 − 2?3 = 2000

−3?1 + 18?2 − 6?3 = 1400

−4?1 − 2?2 + 12?3 = 3000

Calculate and interpret the condition number. Use the row-sum norm. Scale the coefficient matrix (A) so the absolute value of the maximum element in each row is 1 (max magnitude in each row = 1). You may use MATLAB’s inv to find the inverse of the scaled A matrix

Alternative-Fueled Vehicles The table shows the numbers (in thousands) of alternative-fueled

vehicles A in use in the United States from 1995 to 2011. (Source: U.S. Energy Information Administration)

(a) Use a graphing utility to plot the data. Let t represent the year, with t = 5 corresponding to 1995. (b) A model for the data is

4615.36t − 8726.7

1 + 15.01t − 0.542t2, 5 ≤ t ≤ 21

where t = 5 corresponds to 1995. Use the model to estimate the numbers of alternative-fueled vehicles in 1996, 2006, and 2011. How do your answers compare to the original data?

(f ) Use the model to predict the numbers of alternative-fueled vehicles in 2016 and 2017

* Need help to understand F . Should I be using a particular formula

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

A square matrix A is said to be symmetric if its transpose A^T satisfies A^T= A, and a
complex-valued square matrix A is said to be Hermitian if its conjugate transpose A^H =
(A)^T = A^T satisfies A^H = A. Thus, a real-valued square matrix A is symmetric if and
only if it is Hermitian. Which of the following is a vector space?
(a) The set of all n xn real-valued symmetric matrices over R.
(b) The set of all n xn complex-valued symmetric matrices over C.
(c) The set of all nx n complex-valued Hermitian matrices over R.
(d) The set of all n xn complex-valued Hermitian matrices over C.
For each case, either verify that it is a vector space or prove otherwise.

Solve the following problem by Dynamic Programming:
Maximize z = (y1 + 2)^2 + y2 * y3 + (y4 - 5)^2
subject to
y1 + y2 + y3 + y4 <= 5
yi >= 0 and integer, i = 1, 2, 3, 4

Prove that the Jacobi method converges for strictly column-diagonally dominant matrices.

Let p= 11 and 13. (a) Determine all the squares modulo p in (Z/pZ)∗. (b) Using this determine the value of the Legendre symbol(a/p)for all a∈(Z/pZ)∗. (c) For all a∈(Z/pZ)∗, compute a^((p−1)/2) and confirm that a^((p−1)/2)=(a/p).

Part 1: Encrypt the message CINEMA using RSA with n = 17 * 11 and e = 13, use A =10...Z = 35, work in blocks of one letter each.

Part 2: Decrypt the message 088-164-051-164-021-074 using the same parameters from part 1.

1) Who were the key stakeholders involved in, or affected by, the collapse of Enron?

2) Identify the principles and recommendations of ASX Listing Rules that relates to the independence requirements of the auditor, the directors and the Chairman of the board.

3) Explain the key issues in the area of:

1. Related party disclosures
2. Insider trading
3. Executive remuneration
4. Role of independent auditor

4) Identify the role of senior management in the corporate governance in the Enron’s collapse.

inbound taxation questions

True / False Questions

1. Service revenue is sourced based on the location in which such services are rendered.
2. Income tax treaties can generally only result in an increase in the amount of U.S. tax due.
3. The purpose of the foreign tax credit is to reduce international double taxation.
4. Under present law, a trust is considered a US person only if a US court has primary supervision over the trust’s administration and US persons have the authority to control all substantial decisions of the trust.
5. Fixed or determinable, annual or periodical income from foreign sources is subject to Internal Revenue Code section’s 1441 and 1442.

12. You plan to save for your retirement during the next 30 years. To do this, he will invest 700 dollars a month in a stock account and 300 dollars in a bond account. The performance of the stock account is expected to be 11% and the bond account pays 6%. When you retire, you will combine your money in an account with a 9% return. How much can you withdraw each month from your account if you have a 25-year withdrawal period?