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3 years ago

1

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

4 0

Answer:

$9C=5(F-32)$

Step-by-step explanation:

The equation which can convert the temperature from degree Celsius into degree Fahrenheit is given as under

$9C=5(F-32)$

We can solve it further for F as

$9C=5F-5 \times 32$

$9C=5F-160$

$9C+160=5F$

Dividing both sides by 5 we get

$\frac{9C}{5}+32=F$

$F=\frac{9C}{5}+32$

Now substituting values of C in this equation will give us the corresponding values of F

Ex : C=1

$F=\frac{ 9\times 1}{5}+32$

$F=\frac{ 9+160}{5}$

$F=\frac{ 169}{5}$

Hence 1 degree Celsius is $\frac{ 169}{5}$ degree Fahrenheit

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Answer:

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Step-by-step explanation:

Let General Transformation matrix be denoted as T

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General counterclockwise rotation matrix in 2-dimension is given as

$R(\theta)=\left[\begin{array}{ccc}cos\theta & - sin\theta\\sin\theta&cos\theta\\\end{array}\right]$

For clockwise rotation we need to insert θ as negative in the above matrix. Therefore, the resulting matrix is

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as sin(-θ) = -sin (θ) and cos(-θ) = cos (θ)

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$sin(45) = \frac{1}{\sqrt{2} }$ and $cos(45) = \frac{1}{\sqrt{2} }$

$R(-45)=\left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]$

Step 2: Reflection through line y = x

This type of reflection maps (x,y)→(y,x)

Therefore the general matrix is

$R(x,y)=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]$

Step 3: General Transformation Matrix

T = R(x,y) R(-θ)

$T=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} } & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]$

$T = \left[\begin{array}{ccc}-\frac{1}{\sqrt{2} } &\frac{1}{\sqrt{2} }\\\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\end{array}\right]$

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