Answer:

Explanation:
We know that impedance of a RLC circuit is given by 
So
here R is resistance
is inductive reactance and
is capacitive reactance
To minimize the impedance
should be zero we know that 
So 


We know that 
So 

Where f is resonance frequency
Answer:
Correct option : (c) period.
Explanation:
The time that is required for a vibrating object to complete one full cycle is called the time period. If f is the frequency of a wave, then the relation between the frequency and the time period is given by :

These are the characteristics of a wave. Some other characteristics are wavelength, amplitude, intensity etc. So, the correct option is (c) "period".
I’m not sure but when’s the deadline
Answer:
Explanation:
![A=\left[\begin{array}{ccc}3&-9&-3\\-1&2&0\\-2&3&-1\end{array}\right] \\\\R_2\rightarrow 3R_2+R_1,R_3\rightarrow 3R_3+2R_1\\\\=\left[\begin{array}{ccc}3&-9&-3\\0&-3&-3\\0&-9&-9\end{array}\right] \\\\R_3\rightarrow 3R_3-9R_2\\\\=\left[\begin{array}{ccc}3&-9&-3\\0&-3&-3\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-9%26-3%5C%5C-1%262%260%5C%5C-2%263%26-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CR_2%5Crightarrow%203R_2%2BR_1%2CR_3%5Crightarrow%203R_3%2B2R_1%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-9%26-3%5C%5C0%26-3%26-3%5C%5C0%26-9%26-9%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CR_3%5Crightarrow%203R_3-9R_2%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-9%26-3%5C%5C0%26-3%26-3%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
This is the row echelon form of A. This means that only two of the vectors in our set are linearly independent. In other words, the first two vectors alone will span the same subspace of
as all three vectors.
Therefore, the linearly independent spanning set for the subspace is
![\left[\begin{array}{ccc}3\\-1\\-2\end{array}\right] \left[\begin{array}{ccc}-9\\2\\3\end{array}\right] \left[\begin{array}{ccc}3\\0\\-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-1%5C%5C-2%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-9%5C%5C2%5C%5C3%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C0%5C%5C-1%5Cend%7Barray%7D%5Cright%5D)