Complete Question:
Given
at a point. What is the force per unit area at this point acting normal to the surface with
? Are there any shear stresses acting on this surface?
Answer:
Force per unit area, 
There are shear stresses acting on the surface since 
Explanation:
![\sigma = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right]](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%2612%2613%5C%5C12%2611%2615%5C%5C13%2615%2620%5Cend%7Barray%7D%5Cright%5D)
equation of the normal,
![\b n = \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cb%20n%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Traction vector on n, 
![T_n = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]](https://tex.z-dn.net/?f=T_n%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%2612%2613%5C%5C12%2611%2615%5C%5C13%2615%2620%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
![T_n = \left[\begin{array}{ccc}\frac{23}{\sqrt{2} }\\0\\\frac{27}{\sqrt{33} }\end{array}\right]](https://tex.z-dn.net/?f=T_n%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B27%7D%7B%5Csqrt%7B33%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)

To get the Force per unit area acting normal to the surface, find the dot product of the traction vector and the normal.


If the shear stress,
, is calculated and it is not equal to zero, this means there are shear stresses.

![\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - 28( (1/ \sqrt{2} ) \b e_x + (1/ \sqrt{2}) \b e_z)\\\\\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - [ (28/ \sqrt{2} ) \b e_x + (28/ \sqrt{2}) \b e_z]\\\\\tau = \frac{-5}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{5}{\sqrt{2} } \b e_z](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%20%5B%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B33%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z%5D%20-%2028%28%20%281%2F%20%5Csqrt%7B2%7D%20%29%20%5Cb%20e_x%20%2B%20%281%2F%20%5Csqrt%7B2%7D%29%20%5Cb%20e_z%29%5C%5C%5C%5C%5Ctau%20%3D%20%20%5B%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B33%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z%5D%20-%20%5B%20%2828%2F%20%5Csqrt%7B2%7D%20%29%20%5Cb%20e_x%20%2B%20%2828%2F%20%5Csqrt%7B2%7D%29%20%5Cb%20e_z%5D%5C%5C%5C%5C%5Ctau%20%3D%20%20%5Cfrac%7B-5%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B5%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z)

Since
, there are shear stresses acting on the surface.
1. In 2010-2011, the temperature decreased. In 2011-present, the temperature started increasing. From 390 to 405+
2. As the more carbon dioxide increases the temperature also increases with it.
The answer is C I just took this quiz.
Answer:2.55 rad/s
Explanation:
Given
Diameter of ride=5 m
radius(r)=2.5 m
Static friction coefficient range=0.60-1
Here Frictional force will balance weight
And limiting frictional force is provided by Centripetal force

weight of object=mg
Equating two
f=mg




because a chemical change takes time