2. If we rotate P(2, 3) with 0=30° in anti- clockwise direction relative to point C(1, 2), we obtain P'.(sin30° =0.5, cos 30° = 0.9) Please finish the following tasks: (1) Write Point P and C coordinates in homogeneous coordinates; (2' ); (2) Write the rotating matrix R in 3*3 format(2' ); (3) Calculate P' with the rotating matrix R and the point C (3' ). %3D
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- Write a program for reading a square matrix (A) 10,10, then calculate and find the following: 1- the sum of the elements of the upper triangle of the matrix. 2 - The sum of the elements of the lower triangle. 3- The sum of the main diagonal elements of the matrix. 4- The sum of the elements of the perimeter of a matrix.You are given six two-dimensional points shown in the table below. Point x coordinate y coordinate Pi 0.1831 0.1085 p2 0.9624 0.1916 p3 0.0732 0.9594 p4 0.2572 0.6066 p5 0.4476 0.7871 0.2292 0.9489 Use the Euclidean distance to compute the distance matrix M for the six points. Show the results of the complete linkage version of the basic agglomerative hierarchical clustering algorithm. That is, for each iteration of the algorithm, you need to show the found closest two clusters and the updated distance matrix M.Use C Language The Pascal triangle can be used to compute the coefficients of the terms in the expansion (a + b)n. For example, (a + b)2 = a2 + 2ab + b2 where 1, 2, and 1 are coefficients. Write a C program that creates a two-dimensional matrix a representing the Pascal triangle of size n. For example, a Pascal triangle of size 6 is shown below: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
- Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given four diverse integer focuses p1, p2, p3 and p4 on XY matrix. In one stage you can pick one of the focuses pi and move it in one of four ways by one. All in all, if you have picked point pi=(x,y) you can move it to (x,y+1), (x,y−1), (x+1,y) or (x−1,y). Your objective to move focuses so that they will shape a square with sides corresponding to OX and OY tomahawks (a square with side 0 is permitted). What is the base number of steps you want to make such a downer? Input The principal line contains a solitary integer t (1≤t≤104) — the number of experiments. Each experiment comprises of four lines. Each line contains two integers x and y (0≤x,y≤109) — directions of one of the focuses pi=(x,y). All focuses are distinctive in one experiment. Output For each experiment, print the single integer — the base number of steps to make a square.To solve the following system of equations, construct the coefficients matrix and solution of this system of equations as NumPymatrix objects named A and R, respectively.Then take the inverse of the coefficients matrix with A.I and multiply it by the solution matrix R. Write the values of the unknowns x, y, z in the solution matrix you will find with the python programming language. 2x - 3y + z = 1 5x - 4y - z = 2 x + 2z = -1Write a program for matrix operations. The operations are matrix addition, matrix subtraction, and matrix multiplication. Use the concept of functions and create a separate function for matrix operations.
- True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).Q2: Given that R=10; Xc= j5;XI =j10; A1=22-90 ;A2=1.5Z0,f=50HZ, solve the circuit by nodal to find V1 and V2, then plot the vector diagram of V1 and V2. B: Write a program to generate the two matrices A[3][4], B[3][4), then to: 1- Calculate the matrix C[3][4] where: whem A[1]-B[1] 1 when A[]Question 5: Physical properties of six flame-retardant fabric samples were investigated. Consider the accompanying data, where x is a measurement of the stiffness of the fabric (mg-cm) and y is its thickness (mm). X y 7.98 24.52 12.47 6.92 20.71 24.11 0.28 0.65 0.32 0.27 0.57 0.81 (a) Use R to answer the following. Construct a scatterplot such that x is the independent variables and y is the dependent variable. Based on the scatterplot, what are your assumptions about the relationship between these two variables? (b) Calculate (by hand) and interpret the value of the sample correlation coefficient r. Does this agree or disagree with the assumptions you made in part (a)? (c) Use R to answer the following. Fit the simple linear regression model to this data. State the equation of the estimated regression line. (d) Use R to answer the following. Plot the equation of the estimated regression line on top of your scatterplot from part (a). Make sure you include the original scatterplot with…Create a matrix that represents the coordinates of 16 random points in 3D space, find each point's distance to origin, and print the longest distance and the index of this point. (in Python)Write a menu-driven program to read and display a p¥q¥r matrix. Also, find the sum, transpose, and product of the two p*q*r matricesThis problem is on Computer Graphics and is based on the topic 'Perspective Projection'. Please provide a step-by-step solution to the problem and explain the steps. The solution must include the General purpose perspective projection matrix. Question: Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.SEE MORE QUESTIONS