The answers are given already but can u pls give explanation on how they got each answer?

PART A Fill in the blank. Select “A” for Always, “B” for Sometimes, and “C” for Never.

1. A set of 3 vectors from R3 _S(B)_ forms a basis for R3.

2. A set of 2 vectors from R3 _N(C)_ spans R3.

3. A set of 4 vectors from R3 is _N(C)_ linearly independent.

4. A set of 2 vectors from R3 is _S(B)_ linearly independent.

5. If a set of vectors spans a vector space V then it is _S(B)_ a basis for V.

6. If B1 and B2 are two different sets of vectors and each forms a basis for the same vector space, then B1 and B2 _A_ have the same number of vectors.

7. If A is a set consisting of only the zero vector and V is a vector space, then A is _A_ a subspace for V.

8. If S is a linearly independent subset of a vector space V, then a given vector in Span(S) can _A_ be

   expressed uniquely as a linear combination of vectors in S.

Explain or use evidence why each is true or false

If C is any smooth, closed curve then Z C e^{x^2} dx = 0

Let F(x, y) = <P(x, y), Q(x, y)> be a vector field on R 2 and let C be a closed curve formed by the unit circle. If ∂P/∂y = ∂Q/∂x , then R C F · dr = 0.

The coordinate transformation x = u² − v² , y = 2uv maps the quarter-disk S = {(u, v) : u² + v² ≤ 1, v ≥ 0, u ≥ 0} onto the half-disk R = {(x, y) : x² + y² ≤ 1, v ≥ 0}.

If x = g(u, v) and y = h(u, v) is a transformation whose Jacobian is a constant 3, then it must map the square [0, 1] × [0, 1] to a region whose area is 1/3.

The equation in φ = π/12 in spherical coordinates describes a cone in R 3 .

A buck converter is operated from the rectified 230 V ac mains, such that the converter de input voltage
IS
V8 = 325 v ± 20%
A control circuit automatically adjusts the converter duty cycleD, to maintain a constant de output voltage
of V = 240 V de. The de load current I can vary over a 10: 1 range:
lOA::;J:s;lA
The MOSFET has an on-resistance ofO.S Q. The diode conduction loss can be modeled by a 0.7 V
source in series with a 0.2 Q resistor. All other losses can be neglected.
(a) Derive an equivalent circuit that models the converter input and output ports, as well as the loss
elements described above.
(b) Given the range of variation of V8 and I described above, over what range will the duty cycle
vary?
(c) At what operating point (i.e., at what value of V8 and I) is the converter power loss the largest?
What is the value of the efficiency at this operating point?

1. For this question, we define the following vectors: u = (1, 2), v = (−2, 3).

(a) Sketch following vectors on the same set of axes. Make sure to label your axes with a scale. i. 2u ii. −v iii. u + 2v iv. A unit vector which is parallel to v

(b) Let w be the vector satisfying u + v + w = 0 (0 is the zero vector). Draw a diagram showing the geometric relationship between the three vectors u, v and w.

2. Let P 1 and P2 be planes with general equations P1 : −2x + y − 4z = 2, P2 : x + 2y = 7.

(a) Let P3 be a plane which is orthogonal to both P1 and P2. If such a plane P3 exists, give a possible general equation for it. Otherwise, explain why it is not possible to find such a plane. (b) Let ` be a line which is orthogonal to both P1 and P2. If such a line ` exists, give a possible vector equation for it. Otherwise, explain why it is not possible to find such a line.

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My question below

Write a complete program that performs encryption/decryption of a text file. Encryption means you need to scramble the words of a file to become secure. Decryption means you need to apply some rules to an encrypted file in order to find the original file with its original content. An example of encryption is to replace each letter in a file with its consecutive letter in the alphabet. Therefore, ‘a’ is replaced by ‘b’, ‘b’ is replaced by ‘c’ and so on and finally ‘z’ is replaced by ‘a’. Thus, if the file contains the following message:

                                    I am a student at csusm

The encrypted message becomes:

                                    J bn b tuvefou bu dtvtn

Then if you get this encrypted message and the key is 1, it means you need to shift the alphabets in the decrypted message by 1 to the left to get the original message back.

This method is called “rot1” indicating that every alphabet rotates by 1 during the encryption. Similarly, rot10 means every alphabet should be rotated by 10 during encryption.

Another method of encryption is to create cryptogram. A cryptogram is a message or word where each letter is replaced with another letter. For example, the string:

                                    The birds name was squawk

might be scrambled to form

                                    xms kbypo zhqs fho obrhfu

Note that space or any punctuation is not scrambled. In this particular case, ‘T’ was replaced with ’x’, each ‘a’ was replaced with ‘h’. etc. We assume there is no difference between lower case or uppercase. Therefore, you must turn all of the letters of a word into lower case before encrypt it. For example, if your work is “McMaster”, the function (word = “tolower(“McMaster”)) makes word to be equal to “mcmaster”.  

Your job is to write a driver program(look at the program guide to see how to create a driver program)that performs different types of encryption or description. First, you need to ask the user to see if the user wants to do encryption or decryption. If the user wants to do encryption, you should find out if the user wants to use “rot” method or cryptogram method. If the user selects the “rot” method, you need to ask for the encryption key. For example, entering 15, means that the user wants to use “rot15” method to do encryption. If the user selects the cryptogram method, you should open the cryptogram text file called “CryptoKey” where the cryptogram string is stored. The cryptogram string should contain a string of 26 letters where the first letter corresponds to letter ‘a’, the second letter corresponds to letter ‘b’ and so on. For example, your cryptogram file may contain the following message.

                                                uhtxvdepqlzfonkcrwyijsgabm

which means ‘u’ corresponds to ‘a’,  ‘h’ corresponds to ‘b’ and … and finally ‘m’ corresponds to ‘z’.

The same procedure should be followed for decryption. You need to ask the user which method the user wants to use (rot or cryptogram) for encryption. Then write the routines that takes an encrypted file and does the decryption to get the original file back.

You are responsible to use string and vector class in this program. For encryption, you need to read the file to be encrypted into a vector of string and place the words (one word per element) into a vector. Then read the elements of your vector one by one and do the encryption and place the encrypted word into another vector. Finally write the content of encrypted vector to an output file.

For decryption, you need to do the same process which is read the file that contains the encrypted information and place the encrypted words one by one into a vector. Then create another vector so that as you decrypt the information you can place the decrypted words into another vector. Finally, the vector that contains the decrypted words (original message) should be written to an output file.

Here is a message you can do your test:

Psychology is the study of mindand behavior[1][2]. It is an academic disciplineand an applied sciencewhich seeks to understand individuals and groups by establishing general principles and researching specific cases [3][4]. In this field, a professional practitioneror researcher is called a psychologistand can be classified as a social, behavioral, or cognitive scientist. Psychologists attempt to understand the role of mental functionsin individual and social behavior, while also exploring the physiologicaland biologicalprocesses that underlie cognitive functions and behaviors. Psychologists explore concepts such as perception, cognition, attention, emotion, intelligence, phenomenology, motivation, brain functioning, personality, behavior, and interpersonal relationships, including psychological resilience, family resilience, and other areas. Psychologists of diverse orientations also consider the unconscious mind. [5]Psychologists employ empirical methodsto infer causaland correlationalrelationships between psychosocial variables. In addition, or in opposition, to employing empiricaland deductivemethods, some especially clinicaland counselingpsychologists at times rely upon symbolic interpretationand other inductivetechniques. Psychology has been described as a "hub science", [6]with psychological findings linking to research and perspectives from the social sciences, natural sciences, medicine, humanities, and philosophy

Place the above message in a text file called “Original.txt” and test your program based on the following:

Execute your program to run the driver routine. Then do the following:

Encrypt the original message using “rot21” (shifting every alphabet to the right 21) and call the file EncryptRot.txt

Encrypt the original message using the following cryptogram and call the file EncryptCrypto.txt

                              yihtqkcdplzuvwmxsgajbrfeon

Decrypt “EncryptRot.txt” file using “rot21” (shifting every alphabet to the left 21) places and call it “DecryptRot.txt”

Decrypt “EncryptCypto.txt” file using the above cryptogram and call it “DecryptCrypto.txt”

Your “DecryptRot.txt” and “DecryptCrypto.txt” should be similar (not exactly identical) to your “Original.txt” file you used for encryption. For example, in the decrypted files all words are in lower case but it is not necessarily the case in the “Original.txt” file.

Need help with finishing this code please:

string getOriginalFileName();

vector <string> PlaceOriginalIntoVector(const string&);

int DriverProgram();

vector <string> EncVectorUsingRot(const vector <string>&);

vector <string> DecVectorUsingRot(const vector <string>&);

vector <string> EncVectorUsingCrypto(const vector <string>&);

vector <string> DecVectorUsingCrypto(const vector <string>&);

string getOriginalFileName()

{

string fileName;

bool done = false;

while (!done)

{

cout << "What is the Name of the original File? ";

cin >> fileName;

ifstream fin;

fin.open(fileName.data());

if (!fin)

cout << "The file name does not exists. Try again: " << endl;

else

{

done = true;

}

}

return fileName;

}

vector <string> PlaceOriginalIntoVector(const string& OriginalFile)

{

vector <string> V;

ifstream fin;

fin.open(OriginalFile.data());

string word;

while (fin >> word)

V.push_back(word);

return V;

}

int DriverProgram()

{bool done = false;

int choice = 0;

while (!done)

{cout << << endl;

cout << "1: Encrypt using \"rot\" method" << endl;

cout << "2: Decrypt using \"rot\" method" << endl;

cout << "3: Encrypt using \"Cryptogram\" method" << endl;

cout << "4: Decrypt using \"Cryptogram\" method" << endl;

cout << "5: Decrypt using \"Cryptogram\" method" << endl;

cout << "Quit the program" << endl;

cout << "Enter your choice: ";

cin >> choice;

if (choice >= 1 && choice <= 5)

done = true;

else

cout << "Try a number between 1 and 5 as shown above" << endl;

}

return choice;

}

vector <string> EncVectorUsingRot(const vector <string>& OriginalVector)

{

cout << "EncVecUsingRot" << endl;

vector <string> V;

return V;

}

vector <string> DecVectorUsingRot(const vector <string>& EncVecRot)

{

cout << "I am in DecVecUsingRot routine " << endl;

vector <string> V;

return V;

}

vector <string> EncVectorUsingCrypto(const vector <string>& OriginalVector)

{

cout << "I am in EncVecUsingCrypto routine" << endl;

vector <string> V;

return V;

}

vector <string> DecVectorUsingCrypto(const vector <string>& EncVecCrypto)

{

cout << "I am in DecVecUsingCrypto routine" << endl;

vector <string> V;

return V;

}

int main()

{

string OriginalFile = getOriginalFileName();

cout << "The name of the file is: " << OriginalFile << endl;

vector <string> OriginalVector = PlaceOriginalIntoVector(OriginalFile);

int last = OriginalVector.size()-1;

cout << "First word in the file is: " << OriginalVector[0] << endl;

cout << "Last word in the file is: " << OriginalVector[last] << endl;

vector <string> EncVecRot, DecVecRot, EncVecCrypto, DecVecCrypto;

bool done = false;

while (!done)

{

int choice = DriverProgram();

if (choice == 1)

{

cout << "choice is 1: EncUsingRot" << endl;

EncVecRot = EncVectorUsingRot(OriginalVector);

}

else if (choice == 2)

{

cout << "choice is 2: DecUsingRot" << endl;

DecVecRot = DecVectorUsingRot(EncVecRot);

}

else if (choice == 3)

{

cout << "choice is 3: EncUsingCrypto" << endl;

EncVecCrypto = EncVectorUsingCrypto(OriginalVector);

}

else if (choice == 4)

{

cout << "choice is 4: DecUsingCrypto" << endl;

DecVecCrypto = DecVectorUsingRot(EncVecCrypto);

}

else if (choice == 5)

{

cout << "choice is 5: Quiting the program" << endl;

done = true;

}

}

system("pause");

return 0;

}

Assume that, on January 1, 2016, Matsui Co. paid $1,296,000 for its investment in 48,000 shares of Yankee Inc. Further, assume that Yankee has 240,000 total shares of stock issued. The book value and fair value of Yankee's identifiable net assets were both $480,000 at January 1, 2016. The following information pertains to Yankee during 2016:

  

Net income	$240,000
Dividends declared and paid	$72,000
Market price of common stock on 12/31/2016	$29/share

  

What amount would Matsui report in its year-end 2016 balance sheet for its investment in Yankee?

  

$1,608,000.

$1,368,000.

$1,329,600.

None of these answer choices is correct.

On April 1, 2016, Marcus Corporation sells a computer to a customer and agrees to provide technical support for the next six months. The customer pays Marcus Corporation $400 up front on April 1, 2016 and $30 per month for the next six months, with amounts billable and paid on the last day of the month (starting on April 30, 2016). Marcus Corporation sells the computer without the technical support for $500. Marcus also provides technical support services to customers on a stand-alone basis for $20 per month.

What journal entry should Marcus Corporation make on April 1, 2016? What journal entry should Marcus Corporation make on April 30, 2016?

a) On March 1, 2016, Corporation issues a $1,000 par value bond with a 10 percent coupon (paid semi-annually) that matures in exactly two years. If the yield to maturity is 7%, at what price should the bond sale?

b)   If the yield to maturity remains at 7%, at what price should the bond sell on May 1, 2016 (2 months after issue)? what is the dirty price on May 1, 2016?

c) Actions by the Fed cause market interest rates go up. If the yield to maturity increases to 8%, at what price should the bond sell on June 1, 2016 (3 months after issue)? what is the dirty price on June 1, 2016?

Vibrant Company had $930,000 of sales in each of three consecutive years 2016–2018, and it purchased merchandise costing $515,000 in each of those years. It also maintained a $230,000 physical inventory from the beginning to the end of that three-year period. In accounting for inventory, it made an error at the end of year 2016 that caused its year-end 2016 inventory to appear on its statements as $210,000 rather than the correct $230,000.

Required:
1. Determine the correct amount of the company’s gross profit in each of the years 2016–2018.
2. Prepare comparative income statements to show the effect of this error on the company's cost of goods sold and gross profit for each of the years 2016?2018.