Answer: only the third option. [Vector A] dot [vector B + vector C]
The dot between the vectors mean that the operation to perform is the "scalar product", alson known as "dot product".
This operation is only defined between two vectors, not one scalar and one vector.
When you perform, in the first option, the dot product of any ot the first and the second vectors you get a scalar, then you cannot make the dot product of this result with the third vector.
For the second option, when you perform the dot product of vectar B with vector C you get a scalar, then you cannot make the dot product ot this result with the vector A.
The third option indicates that you sum the vectors B and C, whose result is a vector and later you make the dot product of this resulting vector with the vector A. Operation valid.
The fourth option indicates the dot product of a scalar with the vector A, which we already explained that is not defined.
Answer:
191.316 K or -81.684 °C
Explanation:
From general gas law,
P₁V₁/T₁ = P₂V₂/T₂ ................ Equation 1
Where P₁ = Initial pressure, V₁ = Initial volume, T₁ = Initial temperature, P₂ = Final pressure, V₂ = Final volume, T₂ = Final Temperature.
Make T₂ the subject of the equation.
T₂ = P₂V₂T₁/P₁ V₁ ............... Equation 2
Given: P₁ = 5.00×10⁶ Pa, T₁ = 25.0°C = 298 K, P₂ = 1.07×10⁶.
Let: V₁ = y cm³, V₂ = 3y cm³
Substitute into equation 2,
T₂ = (1.07×10⁶×298×3y)/(5.00×10⁶×y)
T₂ =191.316 K.
Hence the final temperature = 191.316 K or -81.684 °C
Answer:
angular velocity = π/2/15×60
= π/ 1800 rad/ s
