Numerade

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(2+2+4+4) In this problem we consider the movement of the knight in a game of chess. If you are unfamiliar with this, please see the reference material for this problem, Figure 10.6.5. The knight we are considering is on the standard 8 imes 8 chessboard. We use the standard notation to references the spaces on this board. For example, a knight located at d4 can move to any of the spaces, c2, e2, f3, b3, b5, f5, c6, e6. We may make a graph as follows. The vertices of this graph correspond to the 64 spaces on the chessboard. Two vertices are connected whenever a knight on one space may move to the other space. For example we see that there is an edge between d4 and c2. Use this graph to answer the following questions. (a) Use Matlab to make a vertex matrix for this problem. Discuss how you made your matrix in Matlab. How do you know your matrix is correct? When you hand in this matrix, give it the name knight and name your file Q3a.mat. Please be sure to do this exactly as described, otherwise the program which tests your matrix will not be able to execute and you will be given no credit. (See Lab 2 for details.) (b) Can a knight that begins on b1, after a series of moves, end on c1? If so, what is the minimum number of moves that this would take? Explain. (c) For a knight that begins on b1 is there any space on the board that it cannot occupy after any series of moves? More generally, for any starting position is there any position to which a knight cannot move to from there? (d) Let the distance between two spaces x,y on the board (relative to a knight's travel) be the minimum number of moves for a knight to move from x to y. Starting at b1, which space(s) is/are the "farthest away" from here? More generally, what is the largest distance between any two spaces on the chess- board for a knight? 3. (2+2+4+4) In this problem we consider the movement of the knqht in a game of chess. If you are unfamiliar with this, please see the reference material for this problem. Figure 10.6.5. The knight we are considering is on the standard 8 8 chessboard. We use the standard notation to references the spaces on this board. 1. 6 a6 b6 c6 de g6 h6 5 a5 b5 c5 f5 g5 h5 a4 4 q4 nA a3 b3 15 3 + For example, a knight located at d4 can move to any of the spaces, c2,e2,f3, b3,b5 f5, c6, e6. We may make a graph as follows. The vertices of this graph correspond to the 64 spaces on the chessboard. Two vertices are connected whenever a knight on one space may move to the other space. For example we see that there is an edge between d4 and c2. Use this graph to answer the following questions. (a) Use Matlab to make a vertex matrix for this problem. Discuss how you made your matrix in Matlab. How do you know your matrix is correct? When you hand in this matrix, give it the name knight and name your file Q3a.mat. Please be sure to do this exactly as described, otherwise the program which tests your matrix will not be able to execute and you will be given no credit. (See Lab 2 for details.) (b) Can a knight that begins on b1, after a series of moves, end on c1? If so, what is the minimum number of moves that this would take? Explain. c) For a knight that begins on bl is there any space on the board that it cannot occupy after any series of moves? More generally, for any starting position is there any position to which a knight cannot move to from there? (d) Let the distance between two spaces x, y on the board (relative to a knight's travel) be the minimum number of moves for a knight to move from to y Starting at b1, which space(s) is/are the farthest away" from here? More generally, what is the largest distance between any two spaces on the chess. board for a knight?

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The following program allows a user to add to and list entries from an ArrayList, which maintains a list of employees. Run the program, and provide input to add three employees' names and related data. Then use the list option to display the list. Modify the program to implement the deleteEmployee method. Run the program again and add, list, delete, and list again various entries.

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1- Implementing a cryptosystem: [4 Marks] Choose one of the following cryptography techniques and implement it using any platform with any programming language you prefer such as Java or Python.... etc. Your program should provide the user with two options Encryption and Decryption, with a simple complete UI to get the input from the user and view the result. You can use any restriction you need for the user's input but you need to clarify that : in the report and for the user, and validate the user input based on your restriction. • DES • AES • RSA 2- Research [3 Marks] Do your research on one of the web application threats, either from the threats discussed in Ch7 or or from other sources, explain it with examples, mention any real threat happening if any, and also explain how to minimize the risk of the threat you chose. Notes: • Your writing should be organized as an article. • Well written and well referenced. • One or maximum two pages. 3- Presentation: [3 Marks] Presentation content will be announced later Notes: • Submission materials: • A report containing: • The Article for Q2 • The description of your implemented cryptosystem Q1: the encryption and decryption processes. • Your source code commented with clear naming • A table with screenshots of all the parts of the code with a very brief description of each part. • Test your program with different input (provide screenshots for each input with the output) • Make sure your code is defensive code against any programming flaws. I.e. check for the input not to be malicious code, and the variables and loops not to cause any problems. • You must reference your work if you used any external sources for the code or report. • Any copying that will be dedicated will cause the assignment grade to be assigned in minus (-5).

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Let $f: X \to Y$ be a function between metric spaces $(X, d)$ and $(Y, \rho)$, and let $K \subseteq X$. (4.1) Let $x_0 \in X$. What does it mean to say that $f$ is continuous at the point $x_0$. (4.2) Prove that the following statements are equivalent. (a) $f$ is continuous. (b) For every subset $A \subseteq X$, $f(\overline{A}) \subseteq \overline{f(A)}$. (c) If $B$ is closed in $Y$, then $f^{-1}(B)$ is closed in $X$. (d) If $D$ is open in $Y$, then $f^{-1}(D)$ is open in $X$. (4.3) Define what $K$ is a compact subset of $X$ means and explain any terminology that you use in your definition. (4.4) If $f$ is continuous and $K$ is compact, use the definition of compactness to show that $f(K)$ is a compact subset of $Y$. (4.5) Suppose that $X$ is a vector space over the field of complex numbers $\mathbb{C}$ with inner product $(\cdot, \cdot)$. Define $||\cdot||: X \to \mathbb{R}$ by $||x|| = \sqrt{(x, x)}$. Use the Cauchy-Bunyakowski-Schwarz (CBS) inequality to show that $||\cdot||$ is a norm on $X$.

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The following model represents the movement of an elastically coupled mechanical system where y1 and y2 represent the displacements of the centers of mass of the coupled objects, u is an external force that moves the system and the rest are construction parameters: $M_1\ddot{y_1} + B_1\dot{y_1} + (K_1 + K_2)y_1 = u + K_1y_2$ $M_2\ddot{y_2} + B_2\dot{y_2} + K_2y_2 = K_2y_1$ A) Draw a block diagram that represents the model of the system. This block diagram must be done using integrating blocks (improper blocks, such as a derivative block, cannot be used). B) From the block diagram above, find the transfer function between u and y2 using block algebra.

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? Find $P_{22}$ $V_g(t)$ 4? 1:2 4? $V_g(t) = 10 \cos{377t} \text{ Volts}$ 2?

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72. In the set (1, 5, x, 10, 15), the integer x is the median. The mean of the five numbers is one less than x. The value of x is F. 6 G. 7 H. 8 J. 9 K. none of these

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Rewrite the expression as a product of four linear factors: $(x^2+x)^2 - 22(x^2 + x) + 40$

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Without using a calculator, compute the sine, cosine, and tangent of $\frac{7\pi}{6}$ by using the reference angle. (Type sqrt(2) for $\sqrt{2}$ and sqrt(3) for $\sqrt{3}$.) What is the reference angle? ____ radians. In what quadrant is this angle? ____ (answer 1, 2, 3, or 4) $\sin(\frac{7\pi}{6}) =$ $\cos(\frac{7\pi}{6}) = $

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Suppose that z varies jointly with x and y. Find the constant of proportionality k if z = 115.2 when y = 4 and x = 18. k = Using the k from above write the variation equation in terms of x and y. z = Using the k from above find z given that y = 8 and x = 43. z = If needed, round answer to 3 decimal places. Enter DNE for Does Not Exist, oo for Infinity

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thomas o.