A dice has its faces marked by symbols θ, δ, ω, ε, η and %. Two positions of the same dice are given below. Which face is opposite to face %?

To find the face opposite to the face with the symbol %, we analyze the two given positions of the same dice.

Let us first list all six symbols marked on the faces of the dice:
θ, δ, ω, ε, η, and %.

Now, we examine the visible faces in each position shown in the image:
1. In the first position of the dice, the visible faces are δ (on the top), θ (on the front-left), and ε (on the front-right).
2. In the second position of the dice, the visible faces are ε (on the top), η (on the front-left), and ω (on the front-right).

Since % is the only symbol not visible in either position, it must occupy one of the hidden positions. By analyzing the orientation and rotation of the common faces between the two views, we can determine the exact pairs of opposite faces:
- The face opposite to δ is η.
- The face opposite to ε is ω.
- The face opposite to % is θ.

Therefore, the face opposite to the face % is θ.