Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Here’s a good photo to reference when converting in the metric system.
Each time you move down a step you move the decimal to the right, each time you move up a step you move the decimal to the left.
We are going from 1.2 kg or kilograms, which is at the very top left of the ladder. To get to mg or milligrams, we would have to make six jumps, so we’d move the decimal over six times.
1.2 > 12. > 120. > 1200. > 12000. > 120000. > 1200000.
So our final answer would be 1,200,000mg.
Answer:
When she stretches her arms out,<em> B) her angular speed ω increases due to her moment of inertia decreasing</em>
Explanation:
The angular momentum of a rotating object is defined as the product of its moment of inertia and angular speed.
<em>L = I ω</em>
<em>where</em>
- <em>L is the angular momentum</em>
- <em>I is the moment of inertia</em>
- <em>ω is the angular speed</em>
<em />
According to the principle of conservation of angular momentum, if there is no external torque, angular momentum of the skater must remain conserved. If the initial and final moment of inertia is <em>I_i and I_f </em>while corresponding angular velocities are <em>ω_i and ω_f , </em>then the principle of conservation of angular momentum can be expressed as the following equation:
<em>(I_f) (ω_f) = (I_i) (ω_i)</em>
<em>ω_f / ω_i = I_i / I_f</em>
<em />
From the expression above, we can see that if the moment of inertia decreases, angular velocity would increase to conserve angular momentum of the skater.
Therefore, When she stretches her arms out,<em> her angular speed ω increases due to her moment of inertia decreasing.</em>
They are toxic and all non metals
