Answer:
Explanation:
Generally, length of vector means the magnitude of the vector.
So, given a vector
R = a•i + b•j + c•k
Then, it magnitude can be caused using
|R|= √(a²+b²+c²)
So, applying this to each of the vector given.
(a) 2i + 4j + 3k
The length is
L = √(2²+4²+3²)
L = √(4+16+9)
L = √29
L = 5.385 unit
(b) 5i − 2j + k
Note that k means 1k
The length is
L = √(5²+(-2)²+1²)
Note that, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
Note that, since there is no component j implies that j component is 0
L = 2i + 0j - 1k
The length is
L = √(2²+0²+(-1)²)
L = √(4+0+1)
L = √5
L = 2.236 unit
(d) 5i
Same as above no is j-component and k-component
L = 5i + 0j + 0k
The length is
L = √(5²+0²+0²)
L = √(25+0+0)
L = √25
L = 5 unit
(e) 3i − 2j − k
The length is
L = √(3²+(-2)²+(-1)²)
L = √(9+4+1)
L = √14
L = 3.742 unit
(f) i + j + k
The length is
L = √(1²+1²+1²)
L = √(1+1+1)
L = √3
L = 1.7321 unit
Answer;
-Tsunami
Explanation;
-Tsunami is a series of large ocean waves (or "wave train") of extremely long wavelength and period, usually generated when a gigantic body of water, such as an ocean, is suddenly displaced on a massive scale by an underwater disturbance such as an earthquake occurring on or near the sea floor or a volcanic eruption.
-After a sudden displacement of a large water volume by seismic activity (earthquake), the ocean floor is raised or dropped and large tsunami waves can be formed by gravitational forces.
To find a general equilibrium point for a spring based on the hook law, it is possible to start from the following premise:
Hook's law is given by:
Where,
k= Spring Constant
Change in Length
F = Force
When there is a Mass we have two force acting at the System:
W= mg
Where W is the force product of the weigth. Then the force net can be defined as,
But we have a system in equilibrium, so
We find the equilibrium for any location when
Answer:
<h2>The pin's final velocity is 5m/s</h2>
Explanation:
Step one:
given data
mass of ball m1=5kg
initial velocity of ball u1=10m/s
mass of pin m2=2kg
initial velocity of pin u2= 0m/s
final velocity of ball v2=8m/s
final velocity of pin v2=?
Step two:
The expression for elastic collision is given as
m1u1+m2u2=m1v1+m2v2
substituting we have
5*10+2*0=5*8+2*v2
50+0=40+2v2
50-40=2v2
10=2v2
divide both sides by 2
v2=10/2
v2=5m/s
The pin's final velocity is 5m/s
The best answer is b) increased turbidity from erosion.
Nonpoint source pollution generally happens as a result of many systems interacting, and is not directly attributed to one event or pollutant. Generally, natural environmental systems participate in pollution of this kind, regardless of whether or not human activity was a factor. Examples include water runoff, or erosion.
The other pollutants listed have a direct cause and direct effect, the animal waste goes directly from the animals to the ground they live on, the car shop directly sumps the oil on the ground, and the oil tank leaks directly into the earth. Erosion causing turbidity is a less direct form of pollution, and is due to the synthesis of several natural phenomena<span />
