Can we recover the metric by knowing volume and area?

Does someone know that what is the definition of area of a manifold? and then

Question: Can we recover the metric by knowing its volume and area?

In the simplest case ($ n=1$ ) I don’t know whether two simple closed curve of the same area and circumference are congruent or not!! Any explanation, proof, reference or counterexample would be very appreciated.

How can Zone of Truth be defeated without the caster knowing?

Zone of Truth contains the following clause:

You know whether each creature succeeds or fails on its saving throw.

In a scenario of checking someone’s loyalty, any countermeasure that allows you to always succeed your save against this spell will alert the caster that you have succeeded the save. They will keep you in the area of the spell until you succeed, or until it’s clear something is stopping you from failing – at which point the caster will tell you to remove whatever that effect is doing this, or have it assumed you are disloyal.

What are all the countermeasures to this spell which:

  1. Don’t allow the spell to affect you
  2. Don’t alert the caster you’re unaffected

Note that to fulfil (1), answers should avoid “you can lie by telling the truth in a ZoT”. A competent interrogator will simply ask direct yes/no questions and assume disloyalty if they are not answered directly.

Is knowing the character enough to determin the representation

Let V be a complex représentation of finite dimension of the symmetric group $ S_n$ and $ χ$ the character of $ V$ .

prove $ V=V\otimes_{\Bbb C}\varepsilon$ iff $ χ(\sigma)=0$ for every odd permutation, where $ \varepsilon$ is the signature.

The prove is straightforward $ χ(\sigma) = χ(\sigma) \varepsilon(\sigma) = – χ(\sigma) \Leftrightarrow χ(\sigma)=0$ .

But I am not sure if $ χ(\sigma) = χ(\sigma) \varepsilon(\sigma)\Leftrightarrow V=V\otimes_{\Bbb C}\varepsilon $ ?

Thank you for your help.

Is it possible to open a locked android device or access it’s files without knowing the password?

I have a Samsung phone which is password protected it also has fingerprint enabled.

I don’t need to know how to open it I just want to know if it’s possible to unlock it or access its files?

There is someone claiming that he can open it without losing any of the data for a certain amount of money?

My laptop screen is broken. What CLI commands can I try to activate my HDMI out, not knowing what my HDMI port is titled?

My laptop screen is completely crushed and doesn’t work. So, I don’t know what my HDMI port is titled. What CLI commands can I try to get my system to display on my external monitor?

I’m on Ubuntu 18.04, with LXDE. The laptop is a common AMD/Radeon HP15 x64.

I’ve searched the forums for answers & tried a number of xrandr commands, but nothing’s working…plus, I can’t list my ports, so I’m just guessing what directions to give in the CLI.

How to prevent someone from logging in into Ubuntu without knowing the password?

I just had my browser tabs changed when I just logged in today, it was Incognito so I can’t tell if I can go back to it, but I’m very confused as to how can someone logged in to my computer without knowing the password. I had many incidents where when I logged in, something has changed even though I’m pretty sure no one can tell the password. I need help as to prevent someone from logging in physically, because right now, I can’t prevent it by moving to a different place because of my circumstances.