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coldgirl [10]
3 years ago
9

Rosa is converting a unit of measure in one system to a unit of measure in another system (1, 760yd)/(1mj) * (0.914m)/(1yd) * (1

sm)/(1, 000m) Which statement about Rosa's calculations is true ?
Mathematics
2 answers:
yawa3891 [41]3 years ago
7 0

Answer:

The following statements are true;

(1) 1, 760 yd/1 mi

(2) 0.914 m/1 yd

Step-by-step explanation:

Assuming that mj is a typing error and the correct option is mi which stands for miles.

(1) 1,760 yd/1 mi

The above statement is true since 1 mile of length is equal to 1,760 yards.

(2) 0.914 m/1 yd

The above statement is true since 1 yard of length is equal to 0.914 meters.

Assuming that sm is a typing error and the correct option is cm which stands for centimeters.

(3) 1 cm/1,000 m

The above statement is not true since 1000 m of length is equal to 100000 cm.

Murljashka [212]3 years ago
6 0

Answer:

The statement about Rosa's calculations that is true is (0.914m)/(1yd).

Step-by-step explanation:

The ratio of meter (m) to yard (yd) is 0.914 : 1.

Therefore, the conversion factor is 0.914 m/1 yd

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alexgriva [62]

Answer:

P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)

Step-by-step explanation:

It is a result that a matrix A is orthogonally diagonalizable if and only if A is a symmetric matrix.  According with the data you provided the matrix should be

A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)

We know that its eigenvalues are \lambda_{1}=-14, \lambda_{2}=-5, where \lambda_{2}=-5 has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle,E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle..

With this in mind we can form the matrices P, D that diagonalizes the matrix A so.

P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)

and

D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)

Observe that the rows of P are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of P dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

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Step-by-step explanation:

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