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The electrothermal instability (also known as the ionization instability) is a magnetohydrodynamic (MHD) instability appearing in ... more

Strategy

Use the equation for linear thermal expansion to calculate the change in length , **ΔL** . Use the coefficient of linear expansion, **α** ,for steel from Table 13.2, and note that the change in temperature, **ΔT** , is **55ºC**

**(b)** convert the change in temperature if Kelvin and Fahrenheit degrees. *****this section is not included in the Reference material*

Discussion

Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates **(-3, 5)**. If the player rotates counterclockwise by **20 degrees**, then the objects in the map will correspondingly rotate **20 degrees** clockwise. Find the new coordinates of the character.

To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by **20 degrees**. To do so, we first need to find the radius of this circle and the original angle.

Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:

To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get

While there are two angles that have this cosine value, the angle of **120.964** degrees is in the second quadrant as desired, so it is the angle we were looking for.

Rotating the point clockwise by **20 degrees**, the angle of the point will decrease to **100.964 degrees**. We can then evaluate the coordinates of the rotated point

For **x** axis:

For **y** axis:

The coordinates of the character on the rotated map will be **(-1.109, 5.725)**

Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen

http://www.opentextbookstore.com/precalc/

Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, ... more

Landauer’s principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that “any ... more

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.

P(x)=ax^2 + bx + c,

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.

P(x)=ax^2 + bx + c,

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, ... more

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. The speed of sound in seawater depends ... more

The Peng–Robinson equation of state (PR EOS) was developed in 1976 at The University of Alberta by Ding-Yu Peng and Donald ... more

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The main span of San Francisco’s Golden Gate Bridge is

1275 mlong at its coldest. The bridge is exposed to temperatures ranging from–15ºCto40ºC.(a)What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.