Calculate the value of Eocell for the following reaction: 2Co3+(aq) + 3Ca(s) --> 2Co(s) + 3Ca2+(aq) Co3+(aq) + 3e– --> Co(s) Eo = 1.54 V Ca2+(aq) + 2e– --> Ca(s) Eo = –2.87 V.

A. –1.33 V

B. +1.33 V

C. –4.41 V

D. –11.6 V

E. +4.41 V

show that for any two vectors u and v in an inner product space

||u+v||^2+||u-v||^2=2(||u||^2+||v||^2)

give a geometric interpretation of this result fot he vector space R^2

Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p

(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V ]

(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]

(c) Give a physical explanation for the difference between the two.

(Note: Since the mole number n is just the particle number N divided by Avogadro’s number, holding one constant is equivalent to holding the other constant.)

The Cauchy-Schwarz Inequality Let u and v be vectors in R 2 .

We wish to prove that ->    (u · v)^ 2 ≤ |u|^ 2 |v|^2 .

This inequality is called the Cauchy-Schwarz inequality and is one of the most important inequalities in linear algebra.

One way to do this to use the angle relation of the dot product (do it!). Another way is a bit longer, but can be considered an application of optimization. First, assume that the two vectors are unit in size and consider the constrained optimization problem:

Maximize u · v

Subject to |u| = 1 |v| = 1.

Note that |u| = 1 is equivalent to |u| 2 = u · u = 1.

(a) Let u = a b and v = c d . Rewrite the above maximization problem in terms of a, b, c, d.

(b) Use Lagrange multipliers to show that u · v is maximized provided u = v.

(c) Explain why the maximum value of u · v must, therefore, be 1.

(d) Find the minimum value of u · v and explain why for any unit vectors u and v we must have |u · v| ≤ 1.

(e) Let u and v be any vectors in R 2 (not necessarily unit). Apply your conclusion above to the vectors: u |u| and v |v| to show that (u · v) ^2 ≤ |u|^ 2 |v|^ 2 .

A basis of a vector space V is a maximal linearly independent set of vectors in V . Similarly, one can view it as a minimal spanning set of vectors in V . Prove that any set S ⊆ V spanning a finite-dimensional vector space V contains a basis of V .

Consider the following reduction potentials:

Mg2+ + 2e- → Mg

E° = -2.37 V

V2+ + 2e- → V

E° = -1.18 V

Cu2+ + e- → Cu+

E° = +0.15 V

Which one of the following reactions will proceed spontaneously?

• Mg2+ + V → V2+ + Mg

• Mg2+ + 2Cu+ → 2Cu2+ + Mg

• V2+ + 2Cu+ → V + 2Cu2+

• V + 2Cu2+ → V2+ + 2Cu+

1. Implement a method that meets the following requirements:

(a) Do not reuse any code for the following:

i. Try to write this method with as few lines of code as you can

ii. Sorts a group of three integers, x,y and z, into decreasing order (they do not have to be in a sequence).

iii. Assume the value in x is less than the value in z. You can also assume there are no duplicates among x, y and z (none of them contain the same value)

iv. Prints a message each time the order of two elements are changed.

v. Prints the list before and after sorting

(b) You can reuse Java API code and module code for the following:

i. Calls mergesort to sort the sequence of numbers into increasing order

ii. Prints the list after the second sorting.

(c) Implement a main method that calls the above methods, demonstrating their use with all applicable printed output

Discuss the major findings/rulings and selection/recruitment implications of the following select court cases.

*Griggs v. Duke Power (1971)
*US v. Georgia Power (1973)
*Spurlock v. United Airlines (1972)
*Watson v. Fort Worth Bank and Trust (1988)
*Rudder v. District of Columbia (1995)
*Frank Ricci et al. v. Hohn DeStefano et al. (2009)
*OFCCP v. Ozark Airlines (1986)
*Gross v. FBL Financial Services (2009)