12 has more factors the 19,21,,23, and 25.
a stretch by 3 and a rotation
Answer:
C
Step-by-step explanation:
Answer:
65.56°
Step-by-step explanation:
We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them
That is let p and q be any two vectors and A be the angle between them
So, p·q=|p|*|q|*cosA
⇒![cosA=\frac{u.v}{|u||v|}](https://tex.z-dn.net/?f=cosA%3D%5Cfrac%7Bu.v%7D%7B%7Cu%7C%7Cv%7C%7D)
Given u=-8i-3j and v=-8i+8j
![|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544](https://tex.z-dn.net/?f=%7Cu%7C%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%20%28-3%29%5E%7B2%7D%7D%20%3D8.544)
![|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137](https://tex.z-dn.net/?f=%7Cv%7C%3D%5Csqrt%7B%28-8%29%5E%7B2%7D%2B%20%288%29%5E%7B2%7D%7D%20%3D11.3137)
let A be angle before u and v
therefore, ![cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}](https://tex.z-dn.net/?f=cosA%3D%5Cfrac%7Bu.v%7D%7B%7Cu%7C%7Cv%7C%7D%3D%5Cfrac%7B%28-8%29%2A%28-8%29%2B%28-3%29%2A%288%29%7D%7B8.544%2A11.3137%7D%20%3D%5Cfrac%7B40%7D%7B96.664%7D)
⇒![A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56](https://tex.z-dn.net/?f=A%3Darccos%28%5Cfrac%7B40%7D%7B96.664%7D%20%29%3Darccos%280.4138%20%29%3D65.56)
Therefore angle between u and v is 65.56°