1. Condition for zero acceleration

For the net acceleration to be zero, the net force must be zero:

$\sum \vec F = 0$

So, the additional force to be applied must be equal in magnitude and opposite in direction to the resultant of the four given forces.

2. Resolve the given forces into x and y components

From the free body diagram, the four forces act only along the $x$ and $y$ directions.

Let the resultant of the given four forces be:

$\vec R = R_x \hat i + R_y \hat j$

On summing the forces along the two axes from the figure, we get:

$R_x = -1\,\text{N}, \qquad R_y = -1\,\text{N}$

Hence,

$\vec R = -\hat i - \hat j$

3. Find the balancing force

To make net force zero, required additional force is:

$\vec F_{\text{add}} = -\vec R = \hat i + \hat j$

So its magnitude is:

$|\vec F_{\text{add}}| = \sqrt{1^2+1^2} = \sqrt{2}\,\text{N}$

4. Find the angle with positive x-axis

Since the force has equal positive $x$ and $y$ components,

$\tan \theta = \frac{1}{1} = 1$

Therefore,

$\theta = 45^\circ$

5. Match with options

The required additional force is:

$\boxed{\sqrt{2}\,\text{N at }45^\circ}$

So the correct option is:

$\boxed{\text{A}}$

6. Comparison with stored answer

Stored correct answer: A
Derived answer: A
So, they agree.