Let T,S : V → W be two linear transformations, and suppose B1 = {v1,...,vn} andB2 = {w1,...,wm} are bases of V and W, respectively.

(c) Show that the vector spaces L(V,W) and Matm×n(F) are isomorphic. (Hint: the function MB1,B2 : L(V,W) → Matm×n(F) is linear by (a) and (b). Show that it is a bijection. A linear transformation is uniquely specified by its action on a basis.)

need clearly proof

1. Calculate the mass fraction stochiometric ratio for the combustion of

n-Butane (C₄H₁₀) in air ( 20% v/v O₂   80% v/v N₂)* ratio 4:1.

Given the following Atomic Weights for the elements and their valencies.*

Element            Symbol         Atomic Weight           Valency

Hydrogen              H                          1                             1

Carbon                  C                         12                            4

Nitrogen                N                         14                            3

Oxygen                  O                         16                            2

*Note these numbers have been rounded for ease of calculation.

Paul purchased a new office computer system on February 15, 2016, at a cost of 8300. He would like to use the General Depreciation System (GDS) straight-line method to depreciate the system and does not want to claim bonus depreciation. Using the half-year convention, compute his 2016 and 2017 depreciation. a. His 2016 Depreciation is $1,660, and his 2017 is $2,656 b. His 2016 is $1453 and 2017 is $1660. c. 2016 is $830 and 2017 is $1660 d. 2016 is $691 and 2017 is $1,384

Depreciation for Partial Periods

Chambers Delivery Company purchased a new delivery truck for $46,200 on April 1, 2016. The truck is expected to have a service life of 10 years or 130,800 miles and a residual value of $4,680. The truck was driven 9,700 miles in 2016 and 13,400 miles in 2017. Chambers computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answers to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be(about the same, higher, or lower) under an accelerated method as compared to the straight-line method. The (activity, double declining,sum of , straight) method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Depreciation for Partial Periods

Bar Delivery Company purchased a new delivery truck for $52,200 on April 1, 2016. The truck is expected to have a service life of 10 years or 144,000 miles and a residual value of $1,920. The truck was driven 9,200 miles in 2016 and 11,300 miles in 2017. Bar computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answer to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be (about the same/higher/lower) under an accelerated method as compared to the straight-line method. The (activity/double-declining balance/straight-line/sum-of-the-years-digits) method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Use the following tax rates and taxable wage bases: Employees' and Employer's OASDI—6.2% both on $127,200; HI—1.45% for employees and employers on the total wages paid. Employees' Supplemental HI of 0.9% on wages in excess of $200,000 was not applicable. Karlie Hastings is a writer (employee) for the Santa Fe Gazette and has an annual salary of $49,000. This year, she also realized net self-employment earnings of $85,000 from a book she wrote. What portion of her self-employment earnings is subject to the two parts of the social security tax? a. OASDI taxable self-employment earnings $ b. HI taxable self-employment earnings $ c. OASDI self-employment tax $ d. HI self-employment tax $

Required information

[The following information applies to the questions displayed below.]
  
In 2018, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2020. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

3. Complete the information required below to prepare a partial balance sheet for 2018 and 2019 showing any items related to the contract. (Do not round intermediate calculations.)

3. Let P be an nxn projection matrix (which means that it satisfies P²=P and P^T=P). The goal of this problem is to show that P as a linear transformation is the orthogonal projection onto the range of P.

(a) Show that if v is in the range of P, then Pv=v.

(b) Show that if v is orthogonal to the range of P then Pv=0. (Hint: PPv lies in the range of P, hence is orthogonal to v. Study the dot product of v with PPv.)

(c) The previous parts show that P and the projection map act the same way on vectors that lie either in the range of P or the orthogonal complement of it. Why does this imply that P and the projection map agree on all vectors?

An absorption column operates at 1 atm to separate compound A from air using pure water as solvent. If the concentration of A in the inlet air stream is 900 ppm and the Henry's law constant for A in water is 1000 atm/ppm:

a) What is the equilibrium line equation? (** draw on chart and label)

If the desired outlet air is to contain 200 ppm compound A:

b) What is (L/V)min? (** draw on chart and label)

c) If the actual operating (L/V) is 1.285(L/V), what is the operating equation? (** draw on chart and label)

d) If the actual operating (L/V) is 1.285(L/V), what is the required number of ideal stages? (** draw on chart)

Consider a thin flat rectangular region that of size 4 x 2 m2 and it is electrically insulated at its four corners. (A)Solve Laplace’s equation  2 V(x,y) = 0 in the rectangular region 0 < x < 4 m and 0 < y < 2 m using the separation of variable technique subject to the following boundary conditions:
V(0,y) = 0
V(4,y) = q(y) = 50 sin (3π y / 2)
V(x,0) = 0
V(x,2) = f(x) =100 sin (π x / 4)
(B) Use the result of part (A) to find the corresponding electric field inside the region.