How to search where nested array elements should have a margin?

Question

Mongoose

There is a homework plan:

const schema = new Schema({
  dateAssign: { type: Date, default: Date.now, index: true },
  teacher: { type: Schema.ObjectId, ref: 'user', index: true },
  lesson: { type: Schema.ObjectId, ref: 'lesson', index: true },
  exercises: [
    { type: Schema.ObjectId, ref: 'exercise' },
  ],
});
mongoose.model('homework', schema)

exercise scheme:

const schema = new Schema({
  block: { type: Schema.ObjectId, ref: 'lessonblock', index: true },
  variant: { type: Schema.ObjectId, ref: 'variant', index: true },
  result: { type: Schema.ObjectId, ref: 'exerciseresult', index: true },
  variables: { type: Schema.Types.Mixed, default: {} },
  start_at: { type: Date },
  lock: { type: Boolean, default: false, index: true },
});
mongoose.model('exercise', schema);

It is necessary to find all the objects of the schema c homeworks such that in the nested array exercises all the elements of the array had the field lock = true;

I tried this, it doesn't work:

const HWs = await Homework.find({ teacher, 'exercises.lock': true }, null, { sort: { dateAssign: -1 }, limit: 20 })